0010.ptx

<exercise masterit-seed="7786" 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> 6 \, {x'} - 8 \, {x} = {x''} \hspace{2em}
           {x} (0)= 3 ,
           {x} '(0)= 10 </me>
      </li>
      <li>
        <me> -64 \, {y} = {y''} \hspace{2em}
           {y} (0)= 2 ,
           {y} '(0)= -32 </me>
      </li>
    </ol>
  </statement>
  <answer>
    <me> {x} = 2 \, e^{\left(4 \, t\right)} + e^{\left(2 \, t\right)} </me>
    <me> {y} = 2 \, \cos\left(8 \, t\right) - 4 \, \sin\left(8 \, t\right) </me>
  </answer>
</exercise>