0000.qti

<item ident="C2-4619" title="C2 | Non-homogeneous first-order linear ODE | ver. 4619">
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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?0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}" alt="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}" title="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}" data-latex="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}"/>
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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?0%20=%20-4%20%5C,%20%7By'%7D%20+%2020%20%5C,%20%7By%7D%20+%2048%20%5C,%20e%5E%7Bt%7D" alt="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}" title="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}" data-latex="0 = -4 \, {y'} + 20 \, {y} + 48 \, e^{t}"&gt;
  &lt;/p&gt;
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            <h4>Partial Answer:</h4>
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              <img style="border:1px #ddd solid;padding:5px;border-radius:5px;" src="https://latex.codecogs.com/svg.latex?{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}" alt="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}" title="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}" data-latex="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}"/>
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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%7B%5Cleft(5%20%5C,%20t%5Cright)%7D%20-%203%20%5C,%20e%5E%7Bt%7D" alt="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}" title="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}" data-latex="{y} = k e^{\left(5 \, t\right)} - 3 \, e^{t}"&gt;
  &lt;/p&gt;
&lt;/div&gt;

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