{"id":86,"date":"2014-02-25T09:42:34","date_gmt":"2014-02-25T14:42:34","guid":{"rendered":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/?p=86"},"modified":"2014-02-25T09:42:34","modified_gmt":"2014-02-25T14:42:34","slug":"checking-something-is-a-solution","status":"publish","type":"post","link":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/checking-something-is-a-solution\/","title":{"rendered":"Checking something is a solution"},"content":{"rendered":"

Consider the ODE \\(y” – 3y’ -4y = t^2 +2\\). In class we came up with a particular solution: \\( Y(t) = -1\/4*t + 2\/8*t – 29\/32\\). Here’s how you can get Sage to check quickly that you are correct.<\/p>\n

t = var('t');
\nY = -1\/4*t^2 + 3\/8*t - 29\/32;
\nY.diff(2) - 3*Y.diff() -4*Y<\/code><\/p>\n

If you enter this in Sage, your output will be \\(t^2 + 2\\), which means \\(Y(t)\\) is a solution to the ODE given above.<\/p>\n","protected":false},"excerpt":{"rendered":"

Consider the ODE \\(y” – 3y’ -4y = t^2 +2\\). In class we came up with a particular solution: \\( Y(t) = -1\/4*t + 2\/8*t – 29\/32\\). Here’s how you can get Sage to check quickly that you are correct. t = var(‘t’); Y = -1\/4*t^2 + 3\/8*t – 29\/32; Y.diff(2) – 3*Y.diff() -4*Y If […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[3],"tags":[],"_links":{"self":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/posts\/86"}],"collection":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/comments?post=86"}],"version-history":[{"count":1,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/posts\/86\/revisions"}],"predecessor-version":[{"id":87,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/posts\/86\/revisions\/87"}],"wp:attachment":[{"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/media?parent=86"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/categories?post=86"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pdhorn.expressions.syr.edu\/spring2014mat414\/wp-json\/wp\/v2\/tags?post=86"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}