{"id":116,"date":"2017-12-05T11:21:43","date_gmt":"2017-12-05T10:21:43","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=116"},"modified":"2017-12-07T17:16:56","modified_gmt":"2017-12-07T16:16:56","slug":"efm-principio-de-superposicion","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=116","title":{"rendered":"EFM: Principio de superposici\u00f3n"},"content":{"rendered":"

Terminamos este apartado estudiando el caso $$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=\\sum_{i=1}^n f_i(x),$$ donde cada $f_i(x)$ es alguna de las funciones dadas en los casos anteriores. Este caso cumple el Teorema de superposici\u00f3n:<\/p>\n

Teorema<\/strong>. Sean $y_1$, $y_2$, …, $y_k$ soluciones de la ecuaci\u00f3n diferencial lineal homog\u00e9nea de orden $n$, $F(x,y,y’,…,y^{(n)})=0$, en un intervalo $I$, entonces la combinaci\u00f3n lineal $$y=c_1y_1, c_2 y_2,\\ldots,c_k y_k$$ en donde $c_i$, $i=1,2,\\ldots,k$ son constantes arbitrarias, tambi\u00e9n es una soluci\u00f3n en el intervalo.\n<\/p><\/blockquote>\n

La soluci\u00f3n, por tanto, ser\u00e1 la suma de las soluciones dadas por la soluciones homog\u00e9nea y la particular obtenida de la ecuaci\u00f3n: $$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=f_i(x)$$<\/p>\n

PAra terminar os dejo un resumen:<\/p>\n

\"\"<\/p>\n

 <\/p>\n\n\n\n
Ejercicio:<\/strong> Resolver $y\u201d+y= xe^x+\\sin 2x$, s.a., y(0)=0, y\u2019(0)=2.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Terminamos este apartado estudiando el caso $$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=\\sum_{i=1}^n f_i(x),$$ donde cada $f_i(x)$ es alguna de las funciones dadas en los casos anteriores. Este caso cumple el Teorema de superposici\u00f3n: Teorema. Sean $y_1$, $y_2$, …, $y_k$ soluciones de la ecuaci\u00f3n diferencial lineal homog\u00e9nea de orden $n$, $F(x,y,y’,…,y^{(n)})=0$, en un intervalo $I$, entonces la combinaci\u00f3n lineal $$y=c_1y_1, c_2… Seguir leyendo EFM: Principio de superposici\u00f3n<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/116"}],"collection":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=116"}],"version-history":[{"count":3,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/116\/revisions"}],"predecessor-version":[{"id":123,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/116\/revisions\/123"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=116"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=116"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=116"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}