{"id":626,"date":"2021-03-26T07:52:55","date_gmt":"2021-03-26T07:52:55","guid":{"rendered":"https:\/\/mxth.dk\/?p=626"},"modified":"2024-01-10T12:23:13","modified_gmt":"2024-01-10T11:23:13","slug":"opgaver-ygx","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=626","title":{"rendered":"Opgaver &#8211; differentialligninger"},"content":{"rendered":"\n<h4 class=\" wp-block-heading has-text-align-center eplus-wrapper\">y\u2019\u2019=g(x)<\/h4>\n\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id626_21ef7e-58 kt-accordion-has-9-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=\"0\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane626_0c4f1a-63\" id=\"DLAO001\"><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\">DLAO001**<\/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-group eplus-wrapper is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group eplus-wrapper is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\" eplus-wrapper\">Unders\u00f8g, om f(x)=1 er l\u00f8sning til differentialligningen<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(y\u2019\u2019+2y\u2019+y=x\\)<\/p>\n<\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane626_9ab2bf-18\" id=\"DLAO002\"><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\">DLAO002*<\/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-group eplus-wrapper is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\" eplus-wrapper\">Unders\u00f8g om y=f(x) er enl\u00f8snning til differentialligningen, n\u00e5r<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(y\u2019\u2019=4y\\)     og     \\(f(x)=3e^{2x}\\)<\/p>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-5 kt-pane626_062e20-53\" id=\"DLAO003\"><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\">DLAO003<\/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\">Funktionen f har lokalt maksimum i (2,3) og er l\u00f8sning til diffentialligningen<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(y\u2019\u2019=-x\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Angiv en regneforskrift for f.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-6 kt-pane626_080578-f2\" id=\"DLAO004\"><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\">DLAO004**<\/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\">Bestem funktionen f, n\u00e5r<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(f\u2019\u2019(x)=sin\\big(\\frac{1}{2}x\\big)\\), \\(f\u2019(x)=1\\) og \\(f(0)=0\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-7 kt-pane626_492fd0-ea\" id=\"DLAO005\"><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\">DLAO005**<\/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\">Bestem en forskrift for , n\u00e5r<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(f\u2019\u2019(x)=e^x+sin(x)+cos(x)\\), \\(f\u2019(0)=1\\) og \\(f(0)=2\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-8 kt-pane626_f24545-69\" id=\"DLAO006\"><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\">DLAO006**<\/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\">Bestem en forskrift for f, n\u00e5r<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(f\u2019\u2019(x)=2+4e^x\\), \\(f\u2019(0)=1\\) og \\(f(0)=0\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-9 kt-pane626_78a68e-ca\" id=\"DLAO007\"><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\">DLAO007*<\/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\">Grafen or f har i (4,3) en tangent med h\u00e6ldningskoefficienten -1. Bestem en forskrift for f, n\u00e5r f er l\u00f8sning til<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(y\u2019\u2019=\\frac{1}{\\sqrt{x}}\\), \\(x&gt;0\\)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Samlig af opgaver til differentialligninger af anden orden.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[24,3,4],"tags":[],"class_list":["post-626","post","type-post","status-publish","format-standard","hentry","category-differentialligninger","category-matematik","category-opgave"],"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\/626","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=626"}],"version-history":[{"count":7,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/626\/revisions"}],"predecessor-version":[{"id":2977,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/626\/revisions\/2977"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=626"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=626"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=626"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}