{"id":90,"date":"2021-07-30T17:11:47","date_gmt":"2021-07-30T17:11:47","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/?post_type=chapter&#038;p=90"},"modified":"2022-11-01T23:07:50","modified_gmt":"2022-11-01T23:07:50","slug":"summary-of-series-solutions-of-differential-equations","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/summary-of-series-solutions-of-differential-equations\/","title":{"raw":"Summary of Series Solutions of Differential Equations","rendered":"Summary of Series Solutions of Differential Equations"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Essential Concepts<\/h3>\r\n<div class=\"PageContent-ny9bj0-0 gLsPXs\" tabindex=\"0\">\r\n<div id=\"main-content\" class=\"MainContent__HideOutline-sc-6yy1if-0 bdVAq sc-bdVaJa ibTDPh\" tabindex=\"-1\" data-dynamic-style=\"false\">\r\n<div id=\"composite-page-27\" class=\"os-eoc os-key-concepts-container\" data-type=\"composite-page\" data-uuid-key=\".key-concepts\">\r\n<div class=\"os-key-concepts\">\r\n<div class=\"os-section-area\"><section id=\"fs-id1170571115987\" class=\"key-concepts\" data-depth=\"1\">\r\n<ul id=\"fs-id1170571115993\" data-bullet-style=\"bullet\">\r\n \t<li>Power series representations of functions can sometimes be used to find solutions to differential equations.<\/li>\r\n \t<li>Differentiate the power series term by term and substitute into the differential equation to find relationships between the power series coefficients.<\/li>\r\n<\/ul>\r\n<\/section><\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<h2>Key Equations<\/h2>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Essential Concepts<\/h3>\n<div class=\"PageContent-ny9bj0-0 gLsPXs\" tabindex=\"0\">\n<div id=\"main-content\" class=\"MainContent__HideOutline-sc-6yy1if-0 bdVAq sc-bdVaJa ibTDPh\" tabindex=\"-1\" data-dynamic-style=\"false\">\n<div id=\"composite-page-27\" class=\"os-eoc os-key-concepts-container\" data-type=\"composite-page\" data-uuid-key=\".key-concepts\">\n<div class=\"os-key-concepts\">\n<div class=\"os-section-area\">\n<section id=\"fs-id1170571115987\" class=\"key-concepts\" data-depth=\"1\">\n<ul id=\"fs-id1170571115993\" data-bullet-style=\"bullet\">\n<li>Power series representations of functions can sometimes be used to find solutions to differential equations.<\/li>\n<li>Differentiate the power series term by term and substitute into the differential equation to find relationships between the power series coefficients.<\/li>\n<\/ul>\n<\/section>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<h2>Key Equations<\/h2>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-90\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Calculus Volume 3. <strong>Authored by<\/strong>: Gilbert Strang, Edwin (Jed) Herman. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/books\/calculus-volume-3\/pages\/1-introduction\">https:\/\/openstax.org\/books\/calculus-volume-3\/pages\/1-introduction<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/\">CC BY-NC-SA: Attribution-NonCommercial-ShareAlike<\/a><\/em>. <strong>License Terms<\/strong>: Access for free at https:\/\/openstax.org\/books\/calculus-volume-3\/pages\/1-introduction<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":16,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Calculus Volume 3\",\"author\":\"Gilbert Strang, Edwin (Jed) Herman\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/books\/calculus-volume-3\/pages\/1-introduction\",\"project\":\"\",\"license\":\"cc-by-nc-sa\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/calculus-volume-3\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-90","chapter","type-chapter","status-publish","hentry"],"part":25,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/90","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":2,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/90\/revisions"}],"predecessor-version":[{"id":481,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/90\/revisions\/481"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/parts\/25"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapters\/90\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/media?parent=90"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/pressbooks\/v2\/chapter-type?post=90"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/contributor?post=90"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/calculus3\/wp-json\/wp\/v2\/license?post=90"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}