{"id":32,"date":"2017-10-23T12:28:06","date_gmt":"2017-10-23T11:28:06","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=32"},"modified":"2017-10-23T12:28:06","modified_gmt":"2017-10-23T11:28:06","slug":"efm-formas-diferenciales-exactas","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=32","title":{"rendered":"EFM: Formas diferenciales exactas"},"content":{"rendered":"<p>En este curso trataremos una forma diferencia exacta como una expresi\u00f3n del tipo<br \/>\n$$M(x,y)dx+N(x,y)dy=0.$$<br \/>\nEn determinados casos esta ecuaci\u00f3n se puede tratar como una ecuaci\u00f3n diferencia de variables separadas. Si la forma es:<br \/>\n$$F_1(x)G_2(y)dx+F_2(x)G_1(y)dy=0,$$ resulta que<br \/>\n$$\\frac{G_1(y)}{G_2(y)}dy=-\\frac{F_1(x)}{F_2(x)}dx,$$<br \/>\nque se puede tratar como la ecuaciones que ya hemos visto<\/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 la ED, $(1+x^4)dy+x(1+4y^2)dx=0, \\; y(1)=0$.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>En este curso trataremos una forma diferencia exacta como una expresi\u00f3n del tipo $$M(x,y)dx+N(x,y)dy=0.$$ En determinados casos esta ecuaci\u00f3n se puede tratar como una ecuaci\u00f3n diferencia de variables separadas. Si la forma es: $$F_1(x)G_2(y)dx+F_2(x)G_1(y)dy=0,$$ resulta que $$\\frac{G_1(y)}{G_2(y)}dy=-\\frac{F_1(x)}{F_2(x)}dx,$$ que se puede tratar como la ecuaciones que ya hemos visto Ejercicio: Resolver la ED, $(1+x^4)dy+x(1+4y^2)dx=0, \\; y(1)=0$.<\/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\/32"}],"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=32"}],"version-history":[{"count":1,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/32\/revisions"}],"predecessor-version":[{"id":33,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/32\/revisions\/33"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=32"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=32"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=32"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}