0006.ptx

<exercise masterit-seed="8522" masterit-slug="C1" masterit-name="Homogeneous first-order linear IVP">
  <statement>
    <p>
Explain how to find the general solution to the given ODE,
and the particular solution to the given IVP.
    </p>
    <me> -4 \, {y'} = 8 \, {y} ,\hspace{1em}
      y\big( \log\left(2\right) \big)= -\frac{3}{4} </me>
    <p>Then show how to verify that your particular solution is correct.</p>
  </statement>
  <answer>
    <me> {y} = k e^{\left(-2 \, t\right)} </me>
    <me> {y} = -3 \, e^{\left(-2 \, t\right)} </me>
  </answer>
</exercise>