0005.tex

\begin{exerciseStatement}


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

\[ 0 = {y''} + 6 \, {y'} + 8 \, {y} - 17 \, \cos\left(5 \, t\right) - 30 \, \sin\left(5 \, t\right) \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{1} e^{\left(-2 \, t\right)} + k_{2} e^{\left(-4 \, t\right)} - \cos\left(5 \, t\right) \]
\end{exerciseAnswer}