0011.tex

\begin{exerciseStatement}


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

\[ -{y''} + 4 \, {y} - 3 \, {y'} + 30 \, \cos\left(5 \, t\right) - 58 \, \sin\left(5 \, t\right) = 0 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{2} e^{\left(-4 \, t\right)} + k_{1} e^{t} + 2 \, \sin\left(5 \, t\right) \]
\end{exerciseAnswer}