{"id":3073,"date":"2024-02-29T12:26:15","date_gmt":"2024-02-29T11:26:15","guid":{"rendered":"https:\/\/mxth.dk\/?p=3073"},"modified":"2026-04-09T22:41:01","modified_gmt":"2026-04-09T20:41:01","slug":"separationsmetoden","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=3073","title":{"rendered":"Separationsmetoden"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Vi vil her se p\u00e5 separation af variable n\u00e5r vi skal l\u00f8se differentialligninger. Det er ikke alle differentialligninger der kan l\u00f8ses p\u00e5 denne m\u00e5de, da de skal have formen<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\({\\mathrm{d}y\\over\\mathrm{d}x}=h(x)\\cdot g(y)\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Differentialligner p\u00e5 denne form kaldes for separable differentialligninger.<\/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_Yf9QIBbA8GF_\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_Yf9QIBbA8GF_<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">med endnu et eksempel: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_fRpTYH2OI3Dk\">https:\/\/sites.google.com\/view\/stenners-matematik\/differentialligninger#h.p_fRpTYH2OI3Dk<\/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:\/\/gymnasiematematika3.systime.dk\/?id=151#c1403\" target=\"_blank\" rel=\"noopener noreferrer\">matA3 239<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=439#c1376\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 4.10<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=439#c1369\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 4.7<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/gymnasiematematika3.systime.dk\/?id=151#c1404\" target=\"_blank\" rel=\"noopener noreferrer\">matA3 242<\/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\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3073_e3547c-51 kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3073_c13e92-c7\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Facit<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3073_a4eeeb-3c kt-accordion-has-4-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3073_ee931e-d1\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matA3 239<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">a, b, d, e, f og h er separable differentialligninger<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3073_2dc191-cb\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 4.10<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(y=-{1\\over {x^2-3}}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3073_97b600-b9\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matA3 242<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(y=\\sqrt{2\\cdot e^x+7}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane3073_1e4eae-68\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 4.7<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(y=(x+1)^2\\)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Vi vil her se p\u00e5 separation af variable n\u00e5r vi skal l\u00f8se differentialligninger. Det er ikke alle differentialligninger der kan l\u00f8ses p\u00e5 denne m\u00e5de, da de skal have formen<\/p>\n<p>\\({\\mathrm{d}y\\over\\mathrm{d}x}=h(x)\\cdot g(y)\\)<\/p>\n<p>Differentialligner p\u00e5 denne form kaldes for separable differentialligninger.<\/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-3073","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\/3073","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=3073"}],"version-history":[{"count":5,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3073\/revisions"}],"predecessor-version":[{"id":3312,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3073\/revisions\/3312"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3073"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3073"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3073"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}