0008.ptx

<exercise masterit-seed="6494" 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> 100 \, {x} = -{x''} \hspace{2em}
           {x} (0)= -2 ,
           {x} '(0)= -50 </me>
      </li>
      <li>
        <me> {y''} + 3 \, {y'} = 10 \, {y} \hspace{2em}
           {y} (0)= 7 ,
           {y} '(0)= -14 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = -2 \, \cos\left(10 \, t\right) - 5 \, \sin\left(10 \, t\right) </me>
    <me> {y} = 3 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-5 \, t\right)} </me>
  </answer>
</exercise>