{"id":2219,"date":"2020-02-05T14:18:10","date_gmt":"2020-02-05T14:18:10","guid":{"rendered":"http:\/\/lash.utrng.edu.mx\/?p=2219"},"modified":"2020-02-06T20:04:44","modified_gmt":"2020-02-06T20:04:44","slug":"ecuaciones-diferenciales","status":"publish","type":"post","link":"https:\/\/lash.utrng.edu.mx\/?p=2219","title":{"rendered":"Ecuaciones Diferenciales"},"content":{"rendered":"\n<p>Si se quiere determinar la posici\u00f3n de una part\u00edcula m\u00f3vil conociendo su velocidad o aceleraci\u00f3n; o bien, dada una sustancia radiactiva que se desintegra, con coeficiente de variaci\u00f3n conocido, se trata de determinar la cantidad de sustancia remanente despu\u00e9s de un tiempo dado. Vemos que en ejemplos como \u00e9stos, se trata de determinar una funci\u00f3n desconocida mediante datos relacionados por una ecuaci\u00f3n que contiene por lo menos una de las derivadas de la funci\u00f3n desconocida. Estas ecuaciones se denominan E<strong>cuaciones Diferenciales<\/strong> y su estudio constituye una de las ramas de la Matem\u00e1tica que tienen m\u00e1s aplicaciones.<\/p>\n\n\n\n<p>Resumiendo podr\u00edamos decir que son Ecuaciones con t\u00e9rminos donde figuran Derivadas o Diferenciales, las podemos ordenar por <strong>Tipo, Orden y Linealidad<\/strong>.<\/p>\n\n\n\n<!--more-->\n\n\n\n<blockquote class=\"wp-block-quote is-layout-flow wp-block-quote-is-layout-flow\"><p><strong>El Orden<\/strong> de una ecuaci\u00f3n diferencial es el correspondiente al de la derivada de mayor indice que figura en ella.<\/p><p><strong>La Soluci\u00f3n<\/strong> de una ecuaci\u00f3n diferencial es toda relaci\u00f3n entre las variables en la que no figuran ni derivadas ni diferenciales y que satisface id\u00e9nticamente a la ecuaci\u00f3n. <strong>La Soluci\u00f3n General<\/strong> de una ecuaci\u00f3n diferencial de orden n, es aquella soluci\u00f3n que contiene el m\u00e1ximo n\u00famero(=n) de constantes arbitrarias<\/p><\/blockquote>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-luminous-vivid-orange-color\"><strong>Tipo<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Ordinarias<\/strong><ul><li>Una Variable independiente<\/li><\/ul><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"92\" height=\"65\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image.png\" alt=\"\" class=\"wp-image-2220\"\/><\/figure><\/div>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Parciales<\/strong><ul><li>M\u00e1s de una variable independiente<\/li><\/ul><\/li><\/ul>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"62\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-1.png\" alt=\"\" class=\"wp-image-2221\"\/><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-luminous-vivid-orange-color\"><strong>Orden<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>1er orden<ul><li>y &#8216; &#8211; 3y = 5x<\/li><\/ul><\/li><li>2do orden<ul><li>y &#8216; &#8216; &#8211; 3y = 5x<\/li><\/ul><\/li><li>3er orden<ul><li> y&#8217; &#8216; &#8216; &#8211; 3y = 5x<\/li><\/ul><\/li><li>4to orden<\/li><\/ul>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"151\" height=\"37\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-3.png\" alt=\"\" class=\"wp-image-2246\"\/><\/figure>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-luminous-vivid-orange-color\"><strong>Linealidad<\/strong><\/p>\n\n\n\n<p>Todas las funciones est\u00e1n igualadas a la variable independiente X y se consideran como Lineales:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><a href=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-5.png\"><img loading=\"lazy\" decoding=\"async\" width=\"914\" height=\"237\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-5.png\" alt=\"\" class=\"wp-image-2250\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-5.png 914w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-5-300x78.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-5-768x199.png 768w\" sizes=\"auto, (max-width: 914px) 100vw, 914px\" \/><\/a><\/figure>\n\n\n\n<p><strong>Ejemplo <\/strong>de la forma anterior:<\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"875\" height=\"86\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-6.png\" alt=\"\" class=\"wp-image-2254\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-6.png 875w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-6-300x29.png 300w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-6-768x75.png 768w\" sizes=\"auto, (max-width: 875px) 100vw, 875px\" \/><\/figure>\n\n\n\n<p> En el ejemplo anterior, solo al cambiar la variable <strong>x<\/strong> por<strong> y<\/strong> al final de la ecuaci\u00f3n:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"190\" height=\"48\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-11.png\" alt=\"\" class=\"wp-image-2263\"\/><\/figure><\/div>\n\n\n\n<p>La ecuaci\u00f3n cambia a ser <strong>No Lineal<\/strong>, as\u00ed mismo si elevamos la variable <strong>y<\/strong>:<\/p>\n\n\n\n<div class=\"wp-block-image is-style-default\"><figure class=\"aligncenter size-large is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-9.png\" alt=\"\" class=\"wp-image-2260\" width=\"353\" height=\"90\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-9.png 353w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-9-300x76.png 300w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><\/figure><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<p class=\"has-text-color has-medium-font-size has-vivid-purple-color\"><strong>Ejemplos:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-media-text alignwide\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"221\" height=\"79\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-12.png\" alt=\"\" class=\"wp-image-2266\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<ul class=\"wp-block-list\"><li>Var. Dep: y<\/li><li>Var. Inde: x<\/li><li>Ordinaria<\/li><li>Primer orden<\/li><li>Lineal<\/li><\/ul>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-media-text alignwide\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"84\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-13.png\" alt=\"\" class=\"wp-image-2267\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-13.png 343w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-13-300x73.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<ul class=\"wp-block-list\"><li>Var. Dep: w<\/li><li>Var. Inde: x, z<\/li><li>Parcial<\/li><li>Segundo Orden<\/li><li>No es Lineal<\/li><\/ul>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<div class=\"wp-block-media-text alignwide\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"239\" height=\"44\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-14.png\" alt=\"\" class=\"wp-image-2268\"\/><\/figure><div class=\"wp-block-media-text__content\">\n<ul class=\"wp-block-list\"><li>Var. Dep: y<\/li><li>Var. Inde: Posible x<\/li><li>Ordinaria<\/li><li>Tercer Orden<\/li><li>No Lineal?<\/li><li>si se despeja a:<ul><li>y\u00bb&#8217;+3y+2y=0<\/li><li>si es Lineal<\/li><\/ul><\/li><\/ul>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p class=\"has-text-color has-background has-medium-font-size has-vivid-red-color has-very-light-gray-background-color\"><strong>Ejercicios<\/strong><\/p>\n\n\n\n<p> Clasifique cada una de las ecuaciones diferenciales, atendiendo los siguientes datos:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>Las <strong>variables dependientes e independientes<\/strong>,<\/li><li><strong>ordinaria <\/strong>o <strong>parcial<\/strong>,<\/li><\/ul>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>El orden<\/strong>,<\/li><li>L<strong>ineal <\/strong>o <strong>no lineal<\/strong><\/li><\/ul>\n\n\n\n<p><strong>a)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"217\" height=\"61\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-15.png\" alt=\"\" class=\"wp-image-2271\"\/><\/figure>\n\n\n\n<p><strong>b)<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"501\" height=\"68\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-16.png\" alt=\"\" class=\"wp-image-2272\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-16.png 501w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-16-300x41.png 300w\" sizes=\"auto, (max-width: 501px) 100vw, 501px\" \/><\/figure>\n\n\n\n<hr class=\"wp-block-separator\"\/>\n\n\n\n<p><strong>c)<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-large is-style-default\"><img loading=\"lazy\" decoding=\"async\" width=\"348\" height=\"85\" src=\"http:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-17.png\" alt=\"\" class=\"wp-image-2275\" srcset=\"https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-17.png 348w, https:\/\/lash.utrng.edu.mx\/wp-content\/uploads\/2020\/02\/image-17-300x73.png 300w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Si se quiere determinar la posici\u00f3n de una part\u00edcula m\u00f3vil conociendo su velocidad o aceleraci\u00f3n; o bien, dada una sustancia radiactiva que se desintegra, con coeficiente de variaci\u00f3n conocido, se trata de determinar la cantidad de sustancia remanente despu\u00e9s de un tiempo dado. Vemos que en ejemplos como \u00e9stos, se trata de determinar una funci\u00f3n &hellip; <a href=\"https:\/\/lash.utrng.edu.mx\/?p=2219\">Seguir leyendo <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[50],"tags":[],"class_list":["post-2219","post","type-post","status-publish","format-standard","hentry","category-primerparcialmatepaing"],"_links":{"self":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2219"}],"version-history":[{"count":17,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2219\/revisions"}],"predecessor-version":[{"id":2282,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=\/wp\/v2\/posts\/2219\/revisions\/2282"}],"wp:attachment":[{"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/lash.utrng.edu.mx\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}