0005.ptx

<exercise masterit-seed="2691" 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> 0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em}
           {x} (0)= 4 ,
           {x} '(0)= 10 </me>
      </li>
      <li>
        <me> -100 \, {y} = {y''} \hspace{2em}
           {y} (0)= 3 ,
           {y} '(0)= -30 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = 3 \, e^{\left(3 \, t\right)} + e^{t} </me>
    <me> {y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right) </me>
  </answer>
</exercise>