{"id":149,"date":"2018-01-09T10:53:20","date_gmt":"2018-01-09T09:53:20","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=149"},"modified":"2018-01-08T11:29:42","modified_gmt":"2018-01-08T10:29:42","slug":"efm-sistemas-no-homogeneos-2","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=149","title":{"rendered":"EFM: Sistemas no homog\u00e9neos. Variaci\u00f3n de par\u00e1metros"},"content":{"rendered":"

Recordemos que partimos de un sistema de ED en la forma matricial $$X’=A\\,X+B(t),$$ donde consideraremos $A$ una matriz cuadrada de valores constantes, y $B(t)$ una matriz de valores constantes o funcionales, no siendo todos cero.<\/p>\n

Si resulta que la soluci\u00f3n de la parte homog\u00e9nea la podemos obtener como $$X_h=\\Phi(t)\\,C,$$ siendo $C$ la matriz de constantes, la soluci\u00f3n general vendr\u00e1 dada mediante
\n$$X=\\Phi(t)\\,C+\\Phi(t)\\int\\Phi^{-1}(t)B(t)dt$$ <\/p>\n\n\n\n
Ejercicio:<\/strong> Resolver el sistema de ED $$X’=\\begin{pmatrix}
\n-3 & 1\\\\
\n2 & -4\\\\
\n\\end{pmatrix}X+\\begin{pmatrix}3t\\\\ e^{-t}\\end{pmatrix}$$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

Recordemos que partimos de un sistema de ED en la forma matricial $$X’=A\\,X+B(t),$$ donde consideraremos $A$ una matriz cuadrada de valores constantes, y $B(t)$ una matriz de valores constantes o funcionales, no siendo todos cero. Si resulta que la soluci\u00f3n de la parte homog\u00e9nea la podemos obtener como $$X_h=\\Phi(t)\\,C,$$ siendo $C$ la matriz de constantes,… Seguir leyendo EFM: Sistemas no homog\u00e9neos. Variaci\u00f3n de par\u00e1metros<\/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\/149"}],"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=149"}],"version-history":[{"count":4,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/149\/revisions"}],"predecessor-version":[{"id":168,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/149\/revisions\/168"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=149"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=149"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=149"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}