Problem 50928. Solve an ODE: separable equation

Created by ChrisR

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{"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=\"dy/dx = f(x)/g(y)\"/></w:customXmlPr><w:r><w:t>\\frac{dy}{dx}=\\frac{f(x)}{g(y)}</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 the initial condition </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></w:customXmlPr><w:r><w:t>y(x_0) = y_0</w:t></w:r></w:customXml><w:r><w:t>.The test suite will ask for the value of the solution </w:t></w:r><w:customXml w:element=\"equation\"><w:customXmlPr><w:attr w:name=\"displayStyle\" w:val=\"false\"/></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:customXmlPr><w:r><w:t>x</w:t></w:r></w:customXml><w:r><w:t>. Functions such as ode45, ode23, and ode15S are not allowed. </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: 118px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407.5px 59px; transform-origin: 407.5px 59px; 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: 384.5px 10.5px; text-align: left; transform-origin: 384.5px 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: 150.433px 7.66667px; transform-origin: 150.433px 7.66667px; unicode-bidi: normal; "><span style="">Solve the following ordinary differential equation:</span></span></div><div style="block-size: 36px; 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: 384.5px 18px; text-align: left; transform-origin: 384.5px 18px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-15px"><img src="data:image/png;base64,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" alt="dy/dx = f(x)/g(y)" style="width: 65px; height: 36px;" width="65" height="36"></span></div><div style="block-size: 43px; 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: 384.5px 21.5px; text-align: left; transform-origin: 384.5px 21.5px; 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: 73.9167px 7.66667px; transform-origin: 73.9167px 7.66667px; unicode-bidi: normal; "><span style="">with the initial condition </span></span><span style="vertical-align:-6px"><img src="data:image/png;base64,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" 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: 156.35px 7.66667px; transform-origin: 156.35px 7.66667px; unicode-bidi: normal; "><span style="">.The test suite will ask for the value of the solution </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: 26.8333px 7.66667px; transform-origin: 26.8333px 7.66667px; unicode-bidi: normal; "><span style=""> at point </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: 84.675px 7.66667px; transform-origin: 84.675px 7.66667px; unicode-bidi: normal; "><span style="">. Functions such as ode45, ode23, and ode15S are not allowed. </span></span></div></div></div>

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Problem 50928. Solve an ODE: separable equation

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Problem 50928. Solve an ODE: separable equation

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