{"id":1374,"date":"2022-01-18T20:52:55","date_gmt":"2022-01-18T20:52:55","guid":{"rendered":"https:\/\/blogs.ugto.mx\/rea\/?p=1374"},"modified":"2022-02-08T18:50:36","modified_gmt":"2022-02-08T18:50:36","slug":"clase-digital-2-ecuaciones-diferenciales-de-primer-orden","status":"publish","type":"post","link":"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-ecuaciones-diferenciales-de-primer-orden\/","title":{"rendered":"Clase digital 2. Ecuaciones diferenciales de primer orden"},"content":{"rendered":"\n\n\n<div class=\"wp-block-cover\" style=\"min-height:284px;aspect-ratio:unset;\"><span aria-hidden=\"true\" class=\"has-background-dim-40 wp-block-cover__gradient-background has-background-dim\"><\/span><img decoding=\"async\" class=\"wp-block-cover__image-background wp-image-1418\" alt=\"\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k.jpg\" style=\"object-position:60% 91%\" data-object-fit=\"cover\" data-object-position=\"60% 91%\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1600\" height=\"1067\" class=\"wp-block-cover__image-background wp-image-1418\" alt=\"\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k.jpg\" style=\"object-position:60% 91%\" data-object-fit=\"cover\" data-object-position=\"60% 91%\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k.jpg 1600w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k-300x200.jpg 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k-1024x683.jpg 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k-768x512.jpg 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k-1536x1024.jpg 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/awzbbvfew3k-272x182.jpg 272w\" sizes=\"auto, (max-width: 1600px) 100vw, 1600px\" \/><\/noscript><div class=\"wp-block-cover__inner-container is-layout-flow wp-block-cover-is-layout-flow\">\n<p class=\"has-text-align-center has-base-3-color has-text-color has-large-font-size wp-block-paragraph\">Ecuaciones diferenciales de primer orden<\/p>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"introduccion\">Introducci\u00f3n<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Hola!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Es un gusto encontrarte nuevamente, espero que est\u00e9s aprendiendo mucho, sobre todo, que tu \u00e1nimo no decaiga y sigas conociendo m\u00e1s acerca de los temas que se te presentan. Te invito a continuar en la segunda clase denominada Ecuaciones CUACIONES DIFERENCIALES DE PRIMER ORDEN del curso de <strong>Ecuaciones Diferenciales.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">En ella, resolveremos ecuaciones diferenciales de primer orden utilizando diferentes m\u00e9todos:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Separaci\u00f3n de variables<\/li><li>La ecuaci\u00f3n homog\u00e9nea<\/li><li>Ecuaciones exactas<\/li><li>El factor integrante<\/li><li>Ecuaciones lineales de primer orden y ecuaciones de Bernoulli<\/li><\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">El m\u00e9todo depender\u00e1 del tipo de ecuaci\u00f3n que se est\u00e9 analizando. Es importante mencionar que para resolver ecuaciones diferenciales se tendr\u00e1 que integrar, y quiz\u00e1 se requiera de alguna t\u00e9cnica especial de integraci\u00f3n, por lo cual, es importante y recomendable que repases el curso de C\u00e1lculo Integral, ya que en este curso aplicaremos las herramientas de integraci\u00f3n ah\u00ed descritas.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Estas operaciones, simples en apariencia, nos servir\u00e1n para entender las relaciones m\u00e1s complejas de este curso, de ah\u00ed su importancia. No olvides que el objetivo es que logres aprender lo mejor posible.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u00a1Te deseo much\u00edsimo \u00e9xito!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"desarrollo-del-tema\">Desarrollo del tema <\/h2>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"metodo-de-separacion-de-variables\">M\u00e9todo de separaci\u00f3n de variables<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver una ecuaci\u00f3n diferencial utilizando el m\u00e9todo de separaci\u00f3n de variables, primero hay que visualizar si sus t\u00e9rminos se pueden separar de manera que, de cada lado de la igualdad quede una funci\u00f3n de una variable con su diferencial. Es decir, tenga la forma de la ecuaci\u00f3n 10, donde podemos despejar para dejar de cada lado de la igualdad una funci\u00f3n de una variable con su diferencial (ver ecuaci\u00f3n 11).<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10-1024x100.png\" alt=\"\" class=\"wp-image-1424\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"100\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10-1024x100.png\" alt=\"\" class=\"wp-image-1424\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10-1024x100.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10-300x29.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10-768x75.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.10.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que la ecuaci\u00f3n diferencial tiene la forma de la ecuaci\u00f3n 11, se puede aplicar la integral en cada lado de la igualdad como lo muestra la ecuaci\u00f3n 12.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21-1024x58.png\" alt=\"\" class=\"wp-image-1427\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"58\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21-1024x58.png\" alt=\"\" class=\"wp-image-1427\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21-1024x58.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21-300x17.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21-768x44.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.21.png 1244w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lo cual dar\u00e1 como resultado la ecuaci\u00f3n 13, donde&nbsp;H(y) y G(x) son antiderivadas.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40-1024x44.png\" alt=\"\" class=\"wp-image-1428\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40-1024x44.png\" alt=\"\" class=\"wp-image-1428\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.40.png 1235w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A continuaci\u00f3n se presenta un ejemplo donde se puede seguir a detalle este m\u00e9todo.<br><br><strong>Ejemplo:<\/strong> Resolver la ecuaci\u00f3n 14<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49-1024x46.png\" alt=\"\" class=\"wp-image-1429\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"46\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49-1024x46.png\" alt=\"\" class=\"wp-image-1429\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49-1024x46.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.02.49.png 1235w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"solucion\"><strong>Soluci\u00f3n<\/strong><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">Primero poner la ecuaci\u00f3n en forma de diferenciales como lo muestra la ecuaci\u00f3n 15<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25-1024x47.png\" alt=\"\" class=\"wp-image-1430\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25-1024x47.png\" alt=\"\" class=\"wp-image-1430\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.25.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Despu\u00e9s despejar de manera que quede de un lado de la igualdad una de las variables con su diferencial, como lo muestra la ecuaci\u00f3n 16.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34-1024x51.png\" alt=\"\" class=\"wp-image-1431\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"51\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34-1024x51.png\" alt=\"\" class=\"wp-image-1431\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34-1024x51.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34-768x38.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.34.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El siguiente paso es integrar ambos lados de la ecuaci\u00f3n como lo muestra la ecuaci\u00f3n 16.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51-1024x44.png\" alt=\"\" class=\"wp-image-1432\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51-1024x44.png\" alt=\"\" class=\"wp-image-1432\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.03.51.png 1234w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente se integra cada lado de la igualdad como lo muestra la ecuaci\u00f3n 17 y utilizando \u00e1lgebra y las leyes de los logaritmos queda como soluci\u00f3n la ecuaci\u00f3n 18<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09-1024x104.png\" alt=\"\" class=\"wp-image-1433\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"104\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09-1024x104.png\" alt=\"\" class=\"wp-image-1433\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09-1024x104.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09-300x31.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09-768x78.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.09.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar m\u00e1s en el tema puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Ecuaciones diferenciales de variables separables | Introducci\u00f3n\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/jA8nVFz94eY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"la-ecuacion-homogenea\">La ecuaci\u00f3n homog\u00e9nea<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Se dice que una funci\u00f3n&nbsp;f es una funci\u00f3n homog\u00e9nea de grado n, si cumple con la propiedad de la ecuaci\u00f3n 19<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18-1024x50.png\" alt=\"\" class=\"wp-image-1435\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18-1024x50.png\" alt=\"\" class=\"wp-image-1435\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18-1024x50.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18-768x37.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.18.png 1238w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Esto es, si en la funci\u00f3n al sustituir en las variables&nbsp;tx e ty se puede separar como lo muestra el lado derecho de la igualdad, entonces es homog\u00e9nea.<br><br><strong>Ejemplo:<\/strong> decir si la funci\u00f3n 20 es homog\u00e9nea<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26-1024x45.png\" alt=\"\" class=\"wp-image-1436\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"45\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26-1024x45.png\" alt=\"\" class=\"wp-image-1436\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26-1024x45.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26-768x34.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.26.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora vamos a sustituir en la ecuaci\u00f3n 20 donde est\u00e9 x por tx y en donde est\u00e9 y por ty, como lo dice la propiedad de la ecuaci\u00f3n 19 y queda la ecuaci\u00f3n 21.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36-1024x42.png\" alt=\"\" class=\"wp-image-1438\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"42\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36-1024x42.png\" alt=\"\" class=\"wp-image-1438\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36-1024x42.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36-768x32.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.36.png 1232w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando&nbsp;t<sup>3<\/sup> en los dos t\u00e9rminos queda la ecuaci\u00f3n 22, con la cual se comprueba que la funci\u00f3n&nbsp; f (x, y) es homogenea de grado 3.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45-1024x42.png\" alt=\"\" class=\"wp-image-1439\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"42\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45-1024x42.png\" alt=\"\" class=\"wp-image-1439\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45-1024x42.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45-768x32.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.45.png 1239w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Una ecuaci\u00f3n diferencial de primer orden como lo muestra la&nbsp; ecuaci\u00f3n 23 es homog\u00e9nea si&nbsp;Mx (x, y) y N (x, y), son funciones homog\u00e9neas del mismo grado.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55-1024x43.png\" alt=\"\" class=\"wp-image-1440\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"43\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55-1024x43.png\" alt=\"\" class=\"wp-image-1440\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55-1024x43.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55-768x32.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.04.55.png 1228w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver una ecuaci\u00f3n diferencial de primer orden por el m\u00e9todo de la ecuaci\u00f3n homog\u00e9nea se deben de seguir los siguientes pasos:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>Tener la ecuaci\u00f3n diferencial como lo muestra la ecuaci\u00f3n 23<\/li><li>Comprobar que es una ecuaci\u00f3n homog\u00e9nea<\/li><li>Realizar un cambio de variable y =ux, &nbsp; o&nbsp; x = vy. Si se utiliza y = ux, entonces dy = udx + xdu y si se utiliza x = vy entonces dx = vdy + ydv.<\/li><li>Resolver por el m\u00e9todo de separaci\u00f3n de variables<\/li><\/ol>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>: Resolver la ecuaci\u00f3n 24 utilizando el m\u00e9todo de la ecuaci\u00f3n homog\u00e9nea<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06-1024x36.png\" alt=\"\" class=\"wp-image-1441\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"36\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06-1024x36.png\" alt=\"\" class=\"wp-image-1441\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06-1024x36.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06-300x10.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06-768x27.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.06.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Soluci\u00f3n<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Siguiendo los pasos del m\u00e9todo de la ecuaci\u00f3n homog\u00e9nea, la ecuaci\u00f3n 24 ya est\u00e1 como lo muestra la ecuaci\u00f3n 23. El siguiente paso es comprobar que sea homog\u00e9nea, para esto hay que verificar que los t\u00e9rminos&nbsp;(x &#8211; y) y x son funciones homog\u00e9neas con la propiedad de la ecuaci\u00f3n 19. La comprobaci\u00f3n del teorema se muestra en las ecuaciones 25 y 26 respectivamente donde las dos funciones son homog\u00e9neas de grado 1, por lo tanto la ecuaci\u00f3n diferencial es homog\u00e9nea.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14-1024x96.png\" alt=\"\" class=\"wp-image-1442\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"96\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14-1024x96.png\" alt=\"\" class=\"wp-image-1442\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14-1024x96.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14-300x28.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14-768x72.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.14.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El siguiente paso es realizar un cambio de variable seg\u00fan convenga por&nbsp;y = ux, &nbsp; o&nbsp; x = vy, en este caso conviene sustituir y = ux, entonces dy = udx + xdu, sustituyendo este cambio de variable en la ecuaci\u00f3n 24, se obtiene la ecuaci\u00f3n 27<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25-1024x35.png\" alt=\"\" class=\"wp-image-1443\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"35\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25-1024x35.png\" alt=\"\" class=\"wp-image-1443\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25-1024x35.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25-300x10.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25-768x26.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.25.png 1238w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Factorizando y realizando una multiplicaci\u00f3n algebraica se obtiene la ecuaci\u00f3n 28<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34-1024x37.png\" alt=\"\" class=\"wp-image-1445\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"37\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34-1024x37.png\" alt=\"\" class=\"wp-image-1445\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34-1024x37.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34-768x28.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.34.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se factorizan los t\u00e9rminos semejantes que contengan las diferenciales y se obtiene la ecuaci\u00f3n 29<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41-1024x42.png\" alt=\"\" class=\"wp-image-1447\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"42\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41-1024x42.png\" alt=\"\" class=\"wp-image-1447\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41-1024x42.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41-768x32.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.41.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se suman t\u00e9rminos semejantes y se obtiene la ecuaci\u00f3n 30<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48-1024x44.png\" alt=\"\" class=\"wp-image-1449\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48-1024x44.png\" alt=\"\" class=\"wp-image-1449\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.05.48.png 1231w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se despeja dejando de un lado de la igualdad cada variable con su diferencial y se obtiene la ecuaci\u00f3n 31<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00-1024x47.png\" alt=\"\" class=\"wp-image-1450\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00-1024x47.png\" alt=\"\" class=\"wp-image-1450\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.00.png 1235w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente se integra en cada lado de la igualdad quedando la ecuaci\u00f3n 32<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12-1024x41.png\" alt=\"\" class=\"wp-image-1451\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"41\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12-1024x41.png\" alt=\"\" class=\"wp-image-1451\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12-1024x41.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12-768x30.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.12.png 1238w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36-1024x95.png\" alt=\"\" class=\"wp-image-1452\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"95\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36-1024x95.png\" alt=\"\" class=\"wp-image-1452\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36-1024x95.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36-300x28.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36-768x71.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.26.36.png 1250w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Despejando y acomodando t\u00e9rminos obtenemos la respuesta en la ecuaci\u00f3n 33<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29-1024x36.png\" alt=\"\" class=\"wp-image-1453\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"36\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29-1024x36.png\" alt=\"\" class=\"wp-image-1453\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29-1024x36.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29-768x27.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.29.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar m\u00e1s en el tema puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"Ecuaciones diferenciales Homog\u00e9neas | Introducci\u00f3n\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/h8JY9daqCBY?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"ecuaciones-diferenciales-exactas\">Ecuaciones diferenciales exactas<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver una ecuaci\u00f3n diferencial utilizando el m\u00e9todo de ecuaciones exactas hay que seguir ciertos pasos:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>La ecuaci\u00f3n diferencial debe de tener la forma que muestra la ecuaci\u00f3n 23.<\/li><li>Deben cumplir el criterio que muestra la ecuaci\u00f3n 33.<\/li><\/ol>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38-1024x50.png\" alt=\"\" class=\"wp-image-1454\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38-1024x50.png\" alt=\"\" class=\"wp-image-1454\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38-1024x50.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38-768x37.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.38.png 1241w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">3. Se propone una de las soluciones ya sea la ecuaci\u00f3n 34 o la ecuaci\u00f3n 35.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47-1024x103.png\" alt=\"\" class=\"wp-image-1455\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"103\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47-1024x103.png\" alt=\"\" class=\"wp-image-1455\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47-1024x103.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47-300x30.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47-768x77.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.47.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">4. Se integra, seg\u00fan corresponda, considerando constante la otra variable. Esto es, si se toma la ecuaci\u00f3n 34 quedar\u00eda como lo muestra la ecuaci\u00f3n 36.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56-1024x45.png\" alt=\"\" class=\"wp-image-1456\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"45\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56-1024x45.png\" alt=\"\" class=\"wp-image-1456\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56-1024x45.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.06.56.png 1241w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14-1024x67.png\" alt=\"\" class=\"wp-image-1457\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"67\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14-1024x67.png\" alt=\"\" class=\"wp-image-1457\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14-1024x67.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14-300x20.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14-768x50.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.14.png 1246w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">5. El resultado de la integral se deriva parcialmente utilizando la otra soluci\u00f3n e igualando la ecuaci\u00f3n, en este caso utilizando la ecuaci\u00f3n 35.<br>6. Se despeja y se encuentra la soluci\u00f3n para g(y) o h(x) seg\u00fan corresponda.<br>7. Se sustituye g(y) en la soluci\u00f3n original.<br>8. Se pone la soluci\u00f3n igualada a una constante.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para entender mejor este m\u00e9todo se ver\u00e1 el siguiente<strong> ejemplo<\/strong>:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Resuelva la ecuaci\u00f3n diferencial mostrada en la ecuaci\u00f3n 37<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25-1024x39.png\" alt=\"\" class=\"wp-image-1458\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25-1024x39.png\" alt=\"\" class=\"wp-image-1458\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25-1024x39.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25-768x30.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.25.png 1245w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<h5 class=\"wp-block-heading\" id=\"solucion\"><strong>Soluci\u00f3n<\/strong><\/h5>\n\n\n\n<p class=\"wp-block-paragraph\">Siguiendo los pasos, cumple con el paso 1 pues la ecuaci\u00f3n tiene ya la forma de la ecuaci\u00f3n 23.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El paso 2 es cumplir el criterio que marca la ecuaci\u00f3n 33, aplicando las derivadas parciales se obtiene la ecuaci\u00f3n 38 y 39 las cuales son igual a 4 y con esto se cumple el criterio se\u00f1alado.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35-1024x112.png\" alt=\"\" class=\"wp-image-1459\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"112\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35-1024x112.png\" alt=\"\" class=\"wp-image-1459\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35-1024x112.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35-300x33.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35-768x84.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.35.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El tercer paso es proponer una soluci\u00f3n, que en este caso ser\u00e1 el de la ecuaci\u00f3n 34, sustituyendo valores se obtiene la ecuaci\u00f3n 40<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48-1024x41.png\" alt=\"\" class=\"wp-image-1460\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"41\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48-1024x41.png\" alt=\"\" class=\"wp-image-1460\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48-1024x41.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48-768x31.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.48.png 1246w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El cuarto paso es integrar, con lo cual se obtiene la ecuaci\u00f3n 41<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56-1024x36.png\" alt=\"\" class=\"wp-image-1461\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"36\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56-1024x36.png\" alt=\"\" class=\"wp-image-1461\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56-1024x36.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56-300x10.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56-768x27.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.07.56.png 1239w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Al integrar con respecto a x, se obtiene la ecuaci\u00f3n 42<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08-1024x52.png\" alt=\"\" class=\"wp-image-1462\" width=\"1024\" height=\"52\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08-1024x52.png\" alt=\"\" class=\"wp-image-1462\" width=\"1024\" height=\"52\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08-1024x52.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08-768x39.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.08.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El quinto paso es derivar parcialmente la ecuaci\u00f3n 42 utilizando la ecuaci\u00f3n 35, con lo cual se obtiene la ecuaci\u00f3n 43<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18-1024x72.png\" alt=\"\" class=\"wp-image-1463\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"72\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18-1024x72.png\" alt=\"\" class=\"wp-image-1463\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18-1024x72.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18-300x21.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18-768x54.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.18.png 1231w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Se tiene que igualar este resultado a&nbsp;Nx,y para que se cumpla la ecuaci\u00f3n 35, con esto se obtiene la ecuaci\u00f3n 44<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27-1024x46.png\" alt=\"\" class=\"wp-image-1464\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"46\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27-1024x46.png\" alt=\"\" class=\"wp-image-1464\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27-1024x46.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.27.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El sexto paso es despejar y encontrar el valor de g(y), para esto primero despejamos g\u2019(x) obteniendo la ecuaci\u00f3n 45<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35-1024x40.png\" alt=\"\" class=\"wp-image-1465\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35-1024x40.png\" alt=\"\" class=\"wp-image-1465\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35-1024x40.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35-768x30.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.35.png 1241w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Despu\u00e9s se integra para obtener el valor de g(y) como lo muestra la ecuaci\u00f3n 46<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44-1024x40.png\" alt=\"\" class=\"wp-image-1466\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44-1024x40.png\" alt=\"\" class=\"wp-image-1466\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44-1024x40.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44-768x30.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.44.png 1239w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente seguimos con el paso 7 donde se sustituye el valor encontrado de g(y) en la ecuaci\u00f3n 42, obteniendo la soluci\u00f3n que se muestra en la ecuaci\u00f3n 47<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51-1024x47.png\" alt=\"\" class=\"wp-image-1467\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51-1024x47.png\" alt=\"\" class=\"wp-image-1467\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.08.51.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar m\u00e1s en el tema puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"M\u00e9todo de soluci\u00f3n de ecuaciones diferenciales exactas. Zill 2.4_1\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/79LU5_r5DjE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"factor-integrante\">Factor integrante<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora se ver\u00e1 el m\u00e9todo de factor integrante para resolver una ecuaci\u00f3n diferencial de primer orden. Para aplicar este m\u00e9todo la ecuaci\u00f3n diferencial debe ser lineal y de la forma de la ecuaci\u00f3n 48.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00-1024x47.png\" alt=\"\" class=\"wp-image-1468\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00-1024x47.png\" alt=\"\" class=\"wp-image-1468\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.00.png 1235w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sin embargo, es necesario que el coeficiente de la derivada sea igual a uno, por esta raz\u00f3n se debe de dividir toda la igualdad entre&nbsp;a1x, quedando la ecuaci\u00f3n 49<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08-1024x59.png\" alt=\"\" class=\"wp-image-1469\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"59\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08-1024x59.png\" alt=\"\" class=\"wp-image-1469\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08-1024x59.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08-300x17.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08-768x45.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.08.png 1240w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27-1024x141.png\" alt=\"\" class=\"wp-image-1470\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"141\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27-1024x141.png\" alt=\"\" class=\"wp-image-1470\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27-1024x141.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27-300x41.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27-768x105.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.27.png 1245w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que la ecuaci\u00f3n tiene la forma de la ecuaci\u00f3n 50, se identifica el t\u00e9rmino P(x) y se elige el factor integrante que muestra la ecuaci\u00f3n 51.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40-1024x53.png\" alt=\"\" class=\"wp-image-1471\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"53\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40-1024x53.png\" alt=\"\" class=\"wp-image-1471\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40-1024x53.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40-300x16.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40-768x40.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.09.40.png 1230w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El siguiente paso, es resolver la ecuaci\u00f3n del factor integrante (ecuaci\u00f3n 51).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Despu\u00e9s de obtener el factor integrante, este factor se multiplica por la ecuaci\u00f3n 50 obteniendo la ecuaci\u00f3n 52.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01-1024x54.png\" alt=\"\" class=\"wp-image-1472\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"54\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01-1024x54.png\" alt=\"\" class=\"wp-image-1472\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01-1024x54.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01-300x16.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01-768x40.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.01.png 1239w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">De la ecuaci\u00f3n 52 se puede observar que el lado izquierdo de la igualdad es la derivada del producto del factor integrante por la variable dependiente, y; esto es, se puede reescribir la ecuaci\u00f3n como lo muestra la ecuaci\u00f3n 53.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11-1024x60.png\" alt=\"\" class=\"wp-image-1473\" width=\"1007\" height=\"59\" \/><noscript><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11-1024x60.png\" alt=\"\" class=\"wp-image-1473\" width=\"1007\" height=\"59\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11-1024x60.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11-300x18.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11-768x45.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.11.png 1234w\" sizes=\"auto, (max-width: 1007px) 100vw, 1007px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente para obtener una soluci\u00f3n se integra ambos lados de la igualdad de la ecuaci\u00f3n 53.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Para comprender mejor este m\u00e9todo se llevar\u00e1 a cabo un ejemplo.<br><br><strong>Ejemplo:<\/strong> Resolver la ecuaci\u00f3n 54.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18-1024x47.png\" alt=\"\" class=\"wp-image-1474\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18-1024x47.png\" alt=\"\" class=\"wp-image-1474\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.18.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver la ecuaci\u00f3n diferencial por el m\u00e9todo de factor integrante, el primer paso es ver si es una ecuaci\u00f3n lineal como lo indica la ecuaci\u00f3n 48 y efectivamente es una ecuaci\u00f3n lineal que tiene la forma de la ecuaci\u00f3n 48.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">El segundo paso es hacer el coeficiente de la derivada igual a uno por lo tanto, se divide toda la ecuaci\u00f3n entre x quedando la ecuaci\u00f3n 55.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29-1024x43.png\" alt=\"\" class=\"wp-image-1475\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"43\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29-1024x43.png\" alt=\"\" class=\"wp-image-1475\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29-1024x43.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29-768x32.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.10.29.png 1243w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">&#8212;&#8212;&#8211; 56 abajo<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04-1024x166.png\" alt=\"\" class=\"wp-image-1476\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"166\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04-1024x166.png\" alt=\"\" class=\"wp-image-1476\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04-1024x166.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04-300x49.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04-768x124.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.04.png 1243w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Una vez que se obtiene el factor integrante, se multiplica por la ecuaci\u00f3n 55, obteniendo la ecuaci\u00f3n 57.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22-1024x44.png\" alt=\"\" class=\"wp-image-1477\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22-1024x44.png\" alt=\"\" class=\"wp-image-1477\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.22.png 1230w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El siguiente paso es poner la ecuaci\u00f3n 57 como lo indica la ecuaci\u00f3n 53 y realizando operaciones algebraicas se obtiene la ecuaci\u00f3n 58.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29-1024x44.png\" alt=\"\" class=\"wp-image-1478\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29-1024x44.png\" alt=\"\" class=\"wp-image-1478\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.29.png 1242w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente, se integran ambos lados de la igualdad de la ecuaci\u00f3n 58, llegando as\u00ed a la soluci\u00f3n que se muestra en la ecuaci\u00f3n 59.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43-1024x39.png\" alt=\"\" class=\"wp-image-1479\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43-1024x39.png\" alt=\"\" class=\"wp-image-1479\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43-1024x39.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43-768x29.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.11.43.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Reacomodando la ecuaci\u00f3n, despejando la variable independiente, queda la soluci\u00f3n de la ecuaci\u00f3n diferencial mostrada en la ecuaci\u00f3n 60.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55-1024x47.png\" alt=\"\" class=\"wp-image-1480\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"47\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55-1024x47.png\" alt=\"\" class=\"wp-image-1480\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55-1024x47.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55-768x35.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.12.55.png 1241w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar m\u00e1s en el tema puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\ud83e\udd13 Factor integrante | Ecuaciones diferenciales lineales | B\u00e1sico | Ejemplos resueltos paso a paso\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/SvXKpSTw-1M?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\" id=\"ecuaciones-lineales-de-primer-orden-y-ecuaciones-de-bernoulli\">Ecuaciones lineales de primer orden y ecuaciones de Bernoulli<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver una ecuaci\u00f3n diferencial utilizando el m\u00e9todo de Bernoulli primeramente hay que recordar qu\u00e9 forma tiene una ecuaci\u00f3n lineal, la cual se mostr\u00f3 anteriormente en la ecuaci\u00f3n 48 y la forma simplificada mostrada en la ecuaci\u00f3n 50.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Una ecuaci\u00f3n de Bernoulli tiene la forma que se muestra en la ecuaci\u00f3n 61, si comparamos la ecuaci\u00f3n 61 y 50 se puede notar que el t\u00e9rmino f(x) esta multiplicado por un factor&nbsp;y<sup>n<\/sup>, adem\u00e1s si n=0 o n=1 se convertir\u00eda en una ecuaci\u00f3n lineal.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03-1024x58.png\" alt=\"\" class=\"wp-image-1481\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"58\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03-1024x58.png\" alt=\"\" class=\"wp-image-1481\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03-1024x58.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03-300x17.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03-768x43.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.03.png 1237w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33-1024x257.png\" alt=\"\" class=\"wp-image-1482\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"257\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33-1024x257.png\" alt=\"\" class=\"wp-image-1482\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33-1024x257.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33-300x75.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33-768x192.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-15.52.33.png 1249w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Ejemplo<\/strong>: Resolver la ecuaci\u00f3n 63<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31-1024x49.png\" alt=\"\" class=\"wp-image-1483\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"49\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31-1024x49.png\" alt=\"\" class=\"wp-image-1483\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31-1024x49.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31-300x14.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31-768x37.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.31.png 1230w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lo primero que hay que hacer es dejar la ecuaci\u00f3n 63 como lo muestra la ecuaci\u00f3n 54, en donde el coeficiente de la derivada tiene que ser igual a uno. Por lo tanto, dividimos ambos lados de la ecuaci\u00f3n entre x, de esta manera se obtiene la ecuaci\u00f3n 57.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48-1024x57.png\" alt=\"\" class=\"wp-image-1484\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"57\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48-1024x57.png\" alt=\"\" class=\"wp-image-1484\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48-1024x57.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48-300x17.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48-768x43.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.13.48.png 1227w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">La ecuaci\u00f3n 56 muestra una ecuaci\u00f3n de Bernoulli donde n=2. El siguiente paso es sustituir n en la ecuaci\u00f3n 55, con lo que se obtiene la ecuaci\u00f3n 58<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00-1024x39.png\" alt=\"\" class=\"wp-image-1485\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00-1024x39.png\" alt=\"\" class=\"wp-image-1485\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00-1024x39.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00-768x29.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.00.png 1234w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Despejando el valor de y se tiene la ecuaci\u00f3n 59<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39-1024x37.png\" alt=\"\" class=\"wp-image-1486\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"37\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39-1024x37.png\" alt=\"\" class=\"wp-image-1486\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39-1024x37.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39-768x28.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.39.png 1245w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">El siguiente paso es derivar la ecuaci\u00f3n 59 para obtener la ecuaci\u00f3n 60.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46-1024x50.png\" alt=\"\" class=\"wp-image-1487\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"50\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46-1024x50.png\" alt=\"\" class=\"wp-image-1487\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46-1024x50.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46-768x37.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.46.png 1235w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finalmente, se sustituye la ecuaci\u00f3n 59 y 60 en la ecuaci\u00f3n 57, con lo cual se obtiene la ecuaci\u00f3n 61<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54-1024x52.png\" alt=\"\" class=\"wp-image-1488\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"52\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54-1024x52.png\" alt=\"\" class=\"wp-image-1488\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54-1024x52.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54-300x15.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54-768x39.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.14.54.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para resolver se tiene que dejar el coeficiente de la derivado igual a 1, por lo cual,hay que dividir toda la ecuaci\u00f3n entre&nbsp;-u<sup>-2<\/sup>, haciendo esto queda la ecuaci\u00f3n 62<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01-1024x44.png\" alt=\"\" class=\"wp-image-1489\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01-1024x44.png\" alt=\"\" class=\"wp-image-1489\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.01.png 1231w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">La ecuaci\u00f3n 62 se convierte en una ecuaci\u00f3n lineal que se puede resolver por el m\u00e9todo del factor integrante, visto en el apartado anterior. Donde el factor integrante se muestra en la ecuaci\u00f3n 63<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08-1024x61.png\" alt=\"\" class=\"wp-image-1490\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"61\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08-1024x61.png\" alt=\"\" class=\"wp-image-1490\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08-1024x61.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08-300x18.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08-768x46.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.08.png 1232w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora se pone la ecuaci\u00f3n 62 como lo indica la ecuaci\u00f3n 53 ya con el factor integrante, con lo que se obtiene la ecuaci\u00f3n 64<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16-1024x55.png\" alt=\"\" class=\"wp-image-1491\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"55\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16-1024x55.png\" alt=\"\" class=\"wp-image-1491\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16-1024x55.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16-300x16.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16-768x41.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.16.png 1234w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Ahora se integra cada lado de la igualdad quedando la ecuaci\u00f3n 65<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22-1024x44.png\" alt=\"\" class=\"wp-image-1492\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"44\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22-1024x44.png\" alt=\"\" class=\"wp-image-1492\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22-1024x44.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22-300x13.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22-768x33.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.22.png 1236w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><figcaption>Despejando u de la ecuaci\u00f3n 65 se obtiene la ecuaci\u00f3n 66<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38-1024x40.png\" alt=\"\" class=\"wp-image-1493\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"40\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38-1024x40.png\" alt=\"\" class=\"wp-image-1493\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38-1024x40.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38-300x12.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38-768x30.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.38.png 1237w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Sabemos de la ecuaci\u00f3n 58 que&nbsp;u=y<sup>-1<\/sup>, as\u00ed que la sustituimos en la ecuaci\u00f3n 66 quedando la ecuaci\u00f3n 67<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48-1024x39.png\" alt=\"\" class=\"wp-image-1494\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"39\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48-1024x39.png\" alt=\"\" class=\"wp-image-1494\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48-1024x39.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48-300x11.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48-768x29.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.48.png 1228w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><figcaption>Despejando y de la ecuaci\u00f3n 67 se obtiene la soluci\u00f3n de la ecuaci\u00f3n diferencial como se ve en la ecuaci\u00f3n 68<\/figcaption><\/figure>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55-1024x54.png\" alt=\"\" class=\"wp-image-1495\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"54\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55-1024x54.png\" alt=\"\" class=\"wp-image-1495\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55-1024x54.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55-300x16.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55-768x40.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-14.15.55.png 1234w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar en el tema de Ecuaci\u00f3n de Bernoulli puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"\ud83d\udc69\u200d\ud83c\udfeb C\u00f3mo resolver una ECUACI\u00d3N DIFERENCIAL de BERNOULLI | Juliana la Profe\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/al4zhWMdgUA?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Para profundizar en los temas vistos y aplicar estrategias generales puedes consultar el siguiente video:<\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio\"><div class=\"wp-block-embed__wrapper\">\n<iframe loading=\"lazy\" title=\"M\u00e9todo para resolver ecuaciones diferenciales lineales de primer orden #Qu\u00e9dateEnCasa\" width=\"1200\" height=\"675\" src=\"https:\/\/www.youtube.com\/embed\/TJcnqjYQ_sU?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe>\n<\/div><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"conclusion\">Conclusi\u00f3n <\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">En resumen, a lo largo de esta clase conociste cinco diferentes m\u00e9todos para resolver una ecuaci\u00f3n diferencial de primer orden. Es conveniente que recuerdes los siguientes puntos que son importantes para el&nbsp; reconocimiento de&nbsp; cada m\u00e9todo:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-1024x568.png\" alt=\"\" class=\"wp-image-1496\" \/><noscript><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"568\" src=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-1024x568.png\" alt=\"\" class=\"wp-image-1496\" srcset=\"https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-1024x568.png 1024w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-300x167.png 300w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-768x426.png 768w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11-1536x853.png 1536w, https:\/\/blogs.ugto.mx\/rea\/wp-content\/uploads\/sites\/71\/2021\/11\/Captura-de-Pantalla-2021-11-11-a-las-16.20.11.png 1677w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/noscript><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Es as\u00ed como concluimos nuestra segunda clase. \u00a1Vas avanzando muy bien, te felicito! No olvides que para concluir la sesi\u00f3n debes hacer la tarea asignada y enviarla. Te encuentro en la siguiente clase, hasta luego.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Introducci\u00f3n \u00a1Hola! Es un gusto encontrarte nuevamente, espero que est\u00e9s aprendiendo mucho, sobre todo, que tu \u00e1nimo no decaiga y sigas conociendo m\u00e1s acerca de los temas que se te presentan. Te invito a continuar en la segunda clase denominada Ecuaciones CUACIONES DIFERENCIALES DE PRIMER ORDEN del curso de Ecuaciones Diferenciales. En ella, resolveremos ecuaciones &#8230; <a title=\"Clase digital 2. Ecuaciones diferenciales de primer orden\" class=\"read-more\" href=\"https:\/\/blogs.ugto.mx\/rea\/clase-digital-2-ecuaciones-diferenciales-de-primer-orden\/\" aria-label=\"Leer m\u00e1s sobre Clase digital 2. Ecuaciones diferenciales de primer orden\">Leer m\u00e1s<\/a><\/p>\n","protected":false},"author":142,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","episode_type":"","audio_file":"","podmotor_file_id":"","podmotor_episode_id":"","cover_image":"","cover_image_id":"","duration":"","filesize":"","filesize_raw":"","date_recorded":"","explicit":"","block":"","itunes_episode_number":"","itunes_title":"","itunes_season_number":"","itunes_episode_type":"","footnotes":""},"categories":[17,21],"tags":[41,80,79],"class_list":["post-1374","post","type-post","status-publish","format-standard","hentry","category-ingenieria-en-comunicaciones-y-electronica","category-uda-ecuaciones-diferenciales-ingenieria-en-comunicaciones-y-electronica","tag-clase-digital","tag-juan-manuel-sierra-hernandez","tag-neli06005"],"acf":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1374","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/users\/142"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/comments?post=1374"}],"version-history":[{"count":5,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1374\/revisions"}],"predecessor-version":[{"id":6860,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/posts\/1374\/revisions\/6860"}],"wp:attachment":[{"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/media?parent=1374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/categories?post=1374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ugto.mx\/rea\/wp-json\/wp\/v2\/tags?post=1374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}