AA5-9.ptx

<exercise checkit-seed="0009" checkit-slug="AA5" checkit-title="Strategies for Solving IVPs">
    <statement>
        <p>
For each ODE, describe an appropriate strategy to find its
general solution, and the features of the ODE that make
that strategy appropriate. (Do not fully solve these ODEs.)
        </p>
        <ol>
                <li>
                    <m>15 \, t = {y'} t - 4 \, {y}</m>
                </li>
                <li>
                    <m>-4 \, {y}^{2} t = 20 \, {y}^{3} {y'} + 4 \, {y} {y'} t^{2} + 10 \, t</m>
                </li>
                <li>
                    <m>-{y''} = -24 \, {y} - 5 \, {y'}</m>
                </li>
                <li>
                    <m>{y''} = 36 \, {y} + 2 \, \mathrm{u}\left(t - 2\right)</m>
                </li>
        </ol>
  </statement>
  <answer>
        <ol>
                <li>
The ODE is linear first-order, so it can be solved by solving its homogeneous form and then using variation of parameters, or using an integrating factor.
                </li>
                <li>
The ODE is exact, so it can be solved by finding a potential function.
                </li>
                <li>
The ODE is linear homogeneous with constant coefficients, so it can be solved by using D-notation and factoring.
                </li>
                <li>
The ODE is linear constant-coefficient with a discontinuous function, so it can be solved by using Laplace transforms.
                </li>
        </ol>
  </answer>
</exercise>