<item ident="F2-7535" title="F2 | Separation of variables | ver. 7535">
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<presentation>
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<div class="exercise-statement">
<p>
<strong>F2.</strong>
</p>
<p>Find the solution to the given IVP.</p>
<p style="text-align:center;">
<img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}"/>
</p>
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<mattext texttype="text/html"><div class="exercise-statement">
<p>
<strong>F2.</strong>
</p>
<p>Find the solution to the given IVP.</p>
<p style="text-align:center;">
<img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?2%20%5C,%20%7By%7D%20%7B%5Cleft(4%20%5C,%20t%20-%201%5Cright)%7D%20+%202%20%5C,%20%7By'%7D%20=%200%20%5Chspace%7B2em%7D%20y(%200%20)=%20-2%20%5C,%20e%5E%7B2%7D" alt="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" title="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}" data-latex="2 \, {y} {\left(4 \, t - 1\right)} + 2 \, {y'} = 0 \hspace{2em} y( 0 )= -2 \, e^{2}">
</p>
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<response_str ident="response1" rcardinality="Single">
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<response_label ident="answer1" rshuffle="No"/>
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<h4>Partial Answer:</h4>
<p style="text-align:center;">
<img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}"/>
</p>
</div>
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<mattext texttype="text/html"><div class="exercise-answer">
<h4>Partial Answer:</h4>
<p style="text-align:center;">
<img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20-2%20%5C,%20e%5E%7B%5Cleft(-2%20%5C,%20t%5E%7B2%7D%20+%20t%20+%202%5Cright)%7D" alt="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" title="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}" data-latex="{y} = -2 \, e^{\left(-2 \, t^{2} + t + 2\right)}">
</p>
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