<exercise masterit-seed="9855" 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''} + 6 \, {y'} = 8 \, {y} - 51 \, \cos\left(5 \, t\right) + 90 \, \sin\left(5 \, t\right) </me>
</statement>
<answer>
<me> {y} = k_{1} e^{\left(4 \, t\right)} + k_{2} e^{\left(2 \, t\right)} - 3 \, \cos\left(5 \, t\right) </me>
</answer>
</exercise>
