0006.ptx

<exercise masterit-seed="4984" masterit-slug="C4" masterit-name="Homogeneous second-order linear IVP">
  <statement>
    <p>Explain how to find the particular solution to each given IVP.</p>
    <ol>
      <li>
        <me> -{x''} = 12 \, {x} + 7 \, {x'} \hspace{2em}
           {x} (0)= -3 ,
           {x} '(0)= 10 </me>
      </li>
      <li>
        <me> -{y''} = 16 \, {y} \hspace{2em}
           {y} (0)= -3 ,
           {y} '(0)= -4 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = -2 \, e^{\left(-3 \, t\right)} - e^{\left(-4 \, t\right)} </me>
    <me> {y} = -3 \, \cos\left(4 \, t\right) - \sin\left(4 \, t\right) </me>
  </answer>
</exercise>