Problem 51387. Solve an ODE: second-order linear equation with constant coefficients

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>Write a function to solve a second-order linear ordinary differential equation with constant coefficients </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>, </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>, 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=\"c\"/></w:customXmlPr><w:r><w:t>c</w:t></w:r></w:customXml><w:r><w:t>: </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=\"ay&quot;+by'+cy = 0\"/></w:customXmlPr><w:r><w:t>a \\frac{d^2y}{dx^2}+b\\frac{dy}{dx}+cy=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 two of the three conditions: (1) </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(x0) = y0\"/></w:customXmlPr><w:r><w:t>y(x_0) = y_0</w:t></w:r></w:customXml><w:r><w:t>, (2) </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'(x0) = y'0\"/></w:customXmlPr><w:r><w:t>y\\prime(x_0) = y\\prime_0</w:t></w:r></w:customXml><w:r><w:t>, and (3) </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(x1) = y1\"/></w:customXmlPr><w:r><w:t>y(x_1) = y_1</w:t></w:r></w:customXml><w:r><w:t>. Two of the three elements of the vector bc will be assigned numerical values, and the third will be </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>NaN</w:t></w:r><w:r><w:t>. The function should return the values of </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 the specified values of </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:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Equations of this form appear in many applications, such as spring-mass-damper systems, RLC circuits, small-amplitude oscillations of a pendulum, and steady advection, dispersion, and decay of a contaminant in a river or groundwater. </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: 190.583px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 95.2917px; transform-origin: 407px 95.2917px; 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: 314.317px 7.91667px; transform-origin: 314.317px 7.91667px; unicode-bidi: normal; "><span style="">Write a function to solve a second-order linear ordinary differential equation with constant coefficients </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">a</span><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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">, </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">b</span><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: 17.5px 7.91667px; transform-origin: 17.5px 7.91667px; unicode-bidi: normal; "><span style="">, and </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">c</span><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: 3.88333px 7.91667px; transform-origin: 3.88333px 7.91667px; unicode-bidi: normal; "><span style="">: </span></span></div><div style="block-size: 37.3333px; 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 18.6667px; text-align: left; transform-origin: 384px 18.6667px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-16px"><img src="data:image/png;base64,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" alt="ay&quot;+by'+cy = 0" style="width: 131.5px; height: 37.5px;" width="131.5" height="37.5"></span></div><div style="block-size: 63.25px; 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 31.625px; text-align: left; transform-origin: 384px 31.625px; 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: 110.458px 7.91667px; transform-origin: 110.458px 7.91667px; unicode-bidi: normal; "><span style="">with two of the three conditions: (1) </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y(x0) = y0" style="width: 64.5px; height: 20px;" width="64.5" height="20"></span><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: 14.3833px 7.91667px; transform-origin: 14.3833px 7.91667px; unicode-bidi: normal; "><span style="">, (2) </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y'(x0) = y'0" style="width: 74px; height: 20px;" width="74" height="20"></span><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: 28px 7.91667px; transform-origin: 28px 7.91667px; unicode-bidi: normal; "><span style="">, and (3) </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" alt="y(x1) = y1" style="width: 64.5px; height: 20px;" width="64.5" height="20"></span><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: 126.783px 7.91667px; transform-origin: 126.783px 7.91667px; unicode-bidi: normal; "><span style="">. Two of the three elements of the vector bc will be assigned numerical values, and the third will be </span></span><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 7.91667px; transform-origin: 11.55px 7.91667px; unicode-bidi: normal; "><span style="font-family: Menlo, Monaco, Consolas, &quot;Courier New&quot;, monospace; ">NaN</span></span><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: 128.742px 7.91667px; transform-origin: 128.742px 7.91667px; unicode-bidi: normal; "><span style="">. The function should return the values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">y</span><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: 50.95px 7.91667px; transform-origin: 50.95px 7.91667px; unicode-bidi: normal; "><span style=""> at the specified values of </span></span><span style="font-family: &quot;STIXGeneral&quot;, &quot;STIXGeneral-webfont&quot;, serif; font-style: italic; font-weight: 400; color: rgb(0, 0, 0);">x</span><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 7.91667px; transform-origin: 1.94167px 7.91667px; unicode-bidi: normal; "><span style="">.</span></span></div><div style="block-size: 42px; 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 21px; text-align: left; transform-origin: 384px 21px; 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: 374.975px 7.91667px; transform-origin: 374.975px 7.91667px; unicode-bidi: normal; "><span style="">Equations of this form appear in many applications, such as spring-mass-damper systems, RLC circuits, small-amplitude oscillations of a pendulum, and steady advection, dispersion, and decay of a contaminant in a river or groundwater. </span></span></div></div></div>

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Problem 51387. Solve an ODE: second-order linear equation with constant coefficients

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Problem 51387. Solve an ODE: second-order linear equation with constant coefficients

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