Explain how to find the general solution to the given ODE.
\[ -{y''} + 6 \, {y'} = 8 \, {y} - 51 \, \cos\left(5 \, t\right) + 90 \, \sin\left(5 \, t\right) \]
Answer:
\[ {y} = k_{1} e^{\left(4 \, t\right)} + k_{2} e^{\left(2 \, t\right)} - 3 \, \cos\left(5 \, t\right) \]