Problem 50609. Solve an ODE: equidimensional equation

Created by ChrisR

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Solve the following ordinary differential equation: </w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"true\"/><w:attr w:name=\"altTextString\" w:val=\"x^2 y''(x) + a x y'(x) + b y(x) = 0\"/></w:customXmlPr><w:r><w:t>x^2 {d^2y\\over dx^2} + a x {dy\\over dx} + b y = 0</w:t></w:r></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>with </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y(x_0) = y_0\"/></w:customXmlPr><w:r><w:t>y(x_0) = y_0</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"dy/dx = y'_0\"/></w:customXmlPr><w:r><w:t>dy/dx = y\\prime_0</w:t></w:r></w:customXml><w:r><w:t> at </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"x = x0\"/></w:customXmlPr><w:r><w:t>x = x_0</w:t></w:r></w:customXml><w:r><w:t>. The parameters </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"a\"/></w:customXmlPr><w:r><w:t>a</w:t></w:r></w:customXml><w:r><w:t> and </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"b\"/></w:customXmlPr><w:r><w:t>b</w:t></w:r></w:customXml><w:r><w:t> are constants, and the value of the function and its derivative at the point </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>x0</w:t></w:r><w:r><w:rPr/><w:t> are specified as </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>y0</w:t></w:r><w:r><w:rPr/><w:t> and </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>yp0</w:t></w:r><w:r><w:rPr/><w:t>, respectively. Your function should return the value of the function </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"y\"/></w:customXmlPr><w:r><w:t>y</w:t></w:r></w:customXml><w:r><w:t> at point </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/><w:attr w:name=\"altTextString\" w:val=\"x\"/></w:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t>.</w:t></w:r></w:p></w:body></w:document>","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 140.45px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 70.225px; transform-origin: 407px 70.225px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 152.375px 7.79167px; transform-origin: 152.375px 7.79167px; unicode-bidi: normal; ">Solve the following ordinary differential equation: </div><div style="block-size: 37.1833px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 18.5917px; text-align: left; transform-origin: 384px 18.5917px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img src="data:image/png;base64,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" alt="x^2 y''(x) + a x y'(x) + b y(x) = 0" style="width: 144px; height: 37px;" width="144" height="37"></div><div style="block-size: 64.2667px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 32.1333px; text-align: left; transform-origin: 384px 32.1333px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 14.3917px 7.79167px; transform-origin: 14.3917px 7.79167px; unicode-bidi: normal; ">with <img src="data:image/png;base64,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" alt="y(x_0) = y_0" style="width: 64.5px; height: 20px;" width="64.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "> and <img src="data:image/png;base64,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" alt="dy/dx = y'_0" style="width: 74.5px; height: 20px;" width="74.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.71667px 7.79167px; transform-origin: 9.71667px 7.79167px; unicode-bidi: normal; "> at <img src="data:image/png;base64,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" alt="x = x0" style="width: 40.5px; height: 20px;" width="40.5" height="20"><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 55.225px 7.79167px; transform-origin: 55.225px 7.79167px; unicode-bidi: normal; ">. The parameters a<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "> and b<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 160.242px 7.79167px; transform-origin: 160.242px 7.79167px; unicode-bidi: normal; "> are constants, and the value of the function and its derivative at the point <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; ">x0<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 52.9px 7.79167px; transform-origin: 52.9px 7.79167px; unicode-bidi: normal; "> are specified as <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 7.7px 7.79167px; transform-origin: 7.7px 7.79167px; unicode-bidi: normal; ">y0<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 15.5583px 7.79167px; transform-origin: 15.5583px 7.79167px; unicode-bidi: normal; "> and <span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 11.55px 7.79167px; transform-origin: 11.55px 7.79167px; unicode-bidi: normal; ">yp0<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.767px 7.79167px; transform-origin: 205.767px 7.79167px; unicode-bidi: normal; ">, respectively. Your function should return the value of the function y<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 9.00833px 7.79167px; transform-origin: 9.00833px 7.79167px; unicode-bidi: normal; "> at point x<span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 1.94167px 7.79167px; transform-origin: 1.94167px 7.79167px; unicode-bidi: normal; ">.</div></div></div>

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Problem 50609. Solve an ODE: equidimensional equation

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