0004.tex

\begin{exerciseStatement}


Explain how to find the general solution to the given ODE.

\[ -{y''} - {y'} + 4 \, \cos\left(2 \, t\right) - 32 \, \sin\left(2 \, t\right) = -12 \, {y} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{1} e^{\left(3 \, t\right)} + k_{2} e^{\left(-4 \, t\right)} + 2 \, \sin\left(2 \, t\right) \]
\end{exerciseAnswer}