0007.ptx

<exercise masterit-seed="6940" 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''} + {x'} = 6 \, {x} \hspace{2em}
           {x} (0)= 9 ,
           {x} '(0)= -2 </me>
      </li>
      <li>
        <me> 36 \, {y} = -{y''} \hspace{2em}
           {y} (0)= 0 ,
           {y} '(0)= 18 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = 5 \, e^{\left(2 \, t\right)} + 4 \, e^{\left(-3 \, t\right)} </me>
    <me> {y} = 3 \, \sin\left(6 \, t\right) </me>
  </answer>
</exercise>