{"id":114,"date":"2017-12-04T11:20:20","date_gmt":"2017-12-04T10:20:20","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=114"},"modified":"2017-12-04T12:41:12","modified_gmt":"2017-12-04T11:41:12","slug":"efm-no-homogenea-con-funciones-trigonometricas","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=114","title":{"rendered":"EFM: No homog\u00e9nea con funciones trigonom\u00e9tricas"},"content":{"rendered":"<p>El siguiente caso trata cuando afrontamos con funciones trigonom\u00e9tricas<br \/>\n$$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=P_1(x)\\, \\cos{rx}+P_2(x)\\, \\sin{rx},$$<br \/>\nen cuyo caso la soluci\u00f3n particular ser\u00e1 de la forma $$y_p=x^s(Q_1(x)\\, \\cos{rx}+Q_2(x)\\, \\sin{rx})$$<\/p>\n<p>Quedar\u00eda ver si ocurre<br \/>\n$$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=(P_1(x)\\, \\cos{bx}+P_2(x)\\, \\sin{bx})e^{ax},$$ que en tal caso la soluci\u00f3n particular depender\u00eda de $a+bi$, y ser\u00eda de la forma<br \/>\n$$y_p=x^s(Q_1(x)\\, \\cos{bx}+Q_2(x)\\, \\sin{bx})e^{ax}$$<\/p>\n<table id=\"yzpi\" width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong> Resolver $y\u201d+y= \\sin 2x$, s.a., y(0)=0, y\u2019(0)=2.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>El siguiente caso trata cuando afrontamos con funciones trigonom\u00e9tricas $$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=P_1(x)\\, \\cos{rx}+P_2(x)\\, \\sin{rx},$$ en cuyo caso la soluci\u00f3n particular ser\u00e1 de la forma $$y_p=x^s(Q_1(x)\\, \\cos{rx}+Q_2(x)\\, \\sin{rx})$$ Quedar\u00eda ver si ocurre $$a\\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=(P_1(x)\\, \\cos{bx}+P_2(x)\\, \\sin{bx})e^{ax},$$ que en tal caso la soluci\u00f3n particular depender\u00eda de $a+bi$, y ser\u00eda de la forma $$y_p=x^s(Q_1(x)\\, \\cos{bx}+Q_2(x)\\, \\sin{bx})e^{ax}$$ Ejercicio: Resolver $y\u201d+y= \\sin 2x$,&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=114\">Seguir leyendo <span class=\"screen-reader-text\">EFM: No homog\u00e9nea con funciones trigonom\u00e9tricas<\/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\/114"}],"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=114"}],"version-history":[{"count":4,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/114\/revisions"}],"predecessor-version":[{"id":121,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/114\/revisions\/121"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=114"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=114"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=114"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}