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>

Solve

Solution Stats

10 Solutions
3 Solvers

Last Solution submitted on May 08, 2022

Last 200 Solutions

Problem Comments

Problem Recent Solvers3

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers3

Suggested Problems

More from this Author183

Problem Tags

Community Treasure Hunt

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

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers3

Suggested Problems

More from this Author183

Problem Tags

Community Treasure Hunt

Players