Explain how to find the general solution to the given ODE.
\[ -5 \, {y'} + {y''} = -6 \, {y} - 57 \, \cos\left(5 \, t\right) + 75 \, \sin\left(5 \, t\right) \]
Answer:
\[ {y} = k_{2} e^{\left(3 \, t\right)} + k_{1} e^{\left(2 \, t\right)} + 3 \, \cos\left(5 \, t\right) \]