<exercise masterit-seed="3235" 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''} + 4 \, {y} - 3 \, {y'} + 30 \, \cos\left(5 \, t\right) - 58 \, \sin\left(5 \, t\right) = 0 </me>
</statement>
<answer>
<me> {y} = k_{2} e^{\left(-4 \, t\right)} + k_{1} e^{t} + 2 \, \sin\left(5 \, t\right) </me>
</answer>
</exercise>
