0008.ptx

<exercise masterit-seed="6305" masterit-slug="C5" masterit-name="Non-homogeneous second-order linear ODE">
  <statement>
    <p>Explain how to find the general solution to the given ODE.</p>
    <me> -5 \, {y'} + {y''} = -6 \, {y} - 57 \, \cos\left(5 \, t\right) + 75 \, \sin\left(5 \, t\right) </me>
  </statement>
  <answer>
    <me> {y} = k_{2} e^{\left(3 \, t\right)} + k_{1} e^{\left(2 \, t\right)} + 3 \, \cos\left(5 \, t\right) </me>
  </answer>
</exercise>