0003.tex

\begin{exerciseStatement}


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

\[ -{y''} - {y'} - 54 \, \cos\left(5 \, t\right) - 10 \, \sin\left(5 \, t\right) = -2 \, {y} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{2} e^{\left(-2 \, t\right)} + k_{1} e^{t} + 2 \, \cos\left(5 \, t\right) \]
\end{exerciseAnswer}