<exercise masterit-seed="0396" 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> -{y''} - {y'} + 4 \, \cos\left(2 \, t\right) - 32 \, \sin\left(2 \, t\right) = -12 \, {y} </me>
</statement>
<answer>
<me> {y} = k_{1} e^{\left(3 \, t\right)} + k_{2} e^{\left(-4 \, t\right)} + 2 \, \sin\left(2 \, t\right) </me>
</answer>
</exercise>
