0006.qti

<item ident="C2-6322" title="C2 | Non-homogeneous first-order linear ODE | ver. 6322">
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          <p>
            <strong>C2.</strong>
          </p>
          <p>Explain how to find the general solution to the given ODE.</p>
          <p style="text-align:center;">
            <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}" alt="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}" title="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}" data-latex="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}"/>
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  &lt;p&gt;
    &lt;strong&gt;C2.&lt;/strong&gt;
  &lt;/p&gt;
  &lt;p&gt;Explain how to find the general solution to the given ODE.&lt;/p&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?32%20%5C,%20%5Ccos%5Cleft(-4%20%5C,%20t%5Cright)%20e%5E%7Bt%7D%20=%204%20%5C,%20%7By%7D%20-%204%20%5C,%20%7By'%7D" alt="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}" title="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}" data-latex="32 \, \cos\left(-4 \, t\right) e^{t} = 4 \, {y} - 4 \, {y'}"&gt;
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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} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)" alt="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)" title="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)" data-latex="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)"/>
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  &lt;h4&gt;Partial Answer:&lt;/h4&gt;
  &lt;p style="text-align:center;"&gt;
    &lt;img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?%7By%7D%20=%20k%20e%5E%7Bt%7D%20+%202%20%5C,%20e%5E%7Bt%7D%20%5Csin%5Cleft(-4%20%5C,%20t%5Cright)" alt="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)" title="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)" data-latex="{y} = k e^{t} + 2 \, e^{t} \sin\left(-4 \, t\right)"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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