0012.ptx

<exercise masterit-seed="3277" 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> -81 \, {x} = {x''} \hspace{2em}
           {x} (0)= 4 ,
           {x} '(0)= 45 </me>
      </li>
      <li>
        <me> 0 = -{y''} - 5 \, {y} - 6 \, {y'} \hspace{2em}
           {y} (0)= 2 ,
           {y} '(0)= -22 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = 4 \, \cos\left(9 \, t\right) + 5 \, \sin\left(9 \, t\right) </me>
    <me> {y} = -3 \, e^{\left(-t\right)} + 5 \, e^{\left(-5 \, t\right)} </me>
  </answer>
</exercise>