0000.tex

\begin{exerciseStatement}


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

\[ {y''} - 2 \, {y'} - 7 \, \cos\left(2 \, t\right) + 4 \, \sin\left(2 \, t\right) = 3 \, {y} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{1} e^{\left(3 \, t\right)} + k_{2} e^{\left(-t\right)} - \cos\left(2 \, t\right) \]
\end{exerciseAnswer}