{"id":2969,"date":"2024-01-10T12:09:51","date_gmt":"2024-01-10T11:09:51","guid":{"rendered":"https:\/\/mxth.dk\/?p=2969"},"modified":"2026-04-09T22:41:01","modified_gmt":"2026-04-09T20:41:01","slug":"eftervisning-af-loesning-til-en-differentialligning","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=2969","title":{"rendered":"Eftervisning af l\u00f8sning til en differentialligning"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Vi skal her se p\u00e5 hvorledes vi kan eftervis at en funktion er en l\u00f8sning til en differentialligning. Vi har tidligere set p\u00e5 hvorledes vi kan finde en l\u00f8sning til differentialligninger p\u00e5 formen \\(y\u2019=g(x)\\) og \\(y\u2019\u2019=g(x)\\). Men her f\u00e5r vi l\u00f8sningen og skal vise at den er en l\u00f8sning til en given differentialligning.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Denne problemstilling er v\u00e6sentlig nemmere da det er nemmere for os at differentiere frem for at integrere, og vi kan derfor arbejde med v\u00e6sentlig sv\u00e6re differentialligninger. <\/p>\n\n\n\n<p class=\" eplus-wrapper\">Her under er der en r\u00e6kke opgaver som d\u00e6kker dette emne.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Link til Stenners side: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_gc-8slSO4XJo\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_gc-8slSO4XJo<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Link til endnu et eksempel: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_D4o6IqYJ4brE\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_D4o6IqYJ4brE<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Og eksempel 3: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_S3t9kALV4gqM\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_S3t9kALV4gqM<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">samt eksempel 4: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_j6FhjCGR4dWm\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_j6FhjCGR4dWm<\/a><\/p>\n\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/matstxa3opgaver.systime.dk\/?id=242#c257\" target=\"_blank\" rel=\"noopener noreferrer\">matAstx 5.01<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxa3opgaver.systime.dk\/?id=242#c274\" target=\"_blank\" rel=\"noopener noreferrer\">matAstx 5.03<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxa3opgaver.systime.dk\/?id=242#c276\" target=\"_blank\" rel=\"noopener noreferrer\">matAstx 5.05<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/matstxa3opgaver.systime.dk\/?id=242#c2113\" target=\"_blank\" rel=\"noopener noreferrer\">matAstx 5.02<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/matstxa3opgaver.systime.dk\/?id=242#c275\" target=\"_blank\" rel=\"noopener noreferrer\">matAstx 5.04<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Vi skal her se p\u00e5 hvorledes vi kan eftervis at en funktion er en l\u00f8sning til en differentialligning. Vi har tidligere set p\u00e5 hvorledes vi kan finde en l\u00f8sning til differentialligninger p\u00e5 formen y\u2019=g(x) og y\u2019\u2019=g(x). Men her f\u00e5r vi l\u00f8sningen og skal vise at den er en l\u00f8sning til en given differentialligning.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[24,3],"tags":[74],"class_list":["post-2969","post","type-post","status-publish","format-standard","hentry","category-differentialligninger","category-matematik","tag-htx"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/2969","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2969"}],"version-history":[{"count":5,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/2969\/revisions"}],"predecessor-version":[{"id":3307,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/2969\/revisions\/3307"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}