Problem 50928. Solve an ODE: separable equation

Created by ChrisR

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<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: 407px 59px; transform-origin: 407px 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: 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: 153px 8px; transform-origin: 153px 8px; 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: 384px 18px; text-align: left; transform-origin: 384px 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: 384px 21.5px; text-align: left; transform-origin: 384px 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: 74.5px 8px; transform-origin: 74.5px 8px; 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: 159px 8px; transform-origin: 159px 8px; 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: 27.5px 8px; transform-origin: 27.5px 8px; 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: 63.5px 8px; transform-origin: 63.5px 8px; unicode-bidi: normal; "><span style="">. Functions such as ode45, ode23, and ode15S are not allowed. </span></span></div></div></div>

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differential equations separable

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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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