0006.tex

\begin{exerciseStatement}


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

\[ 2 \, {y'} + {y''} = 8 \, {y} + 18 \, \cos\left(3 \, t\right) - 51 \, \sin\left(3 \, t\right) \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{1} e^{\left(2 \, t\right)} + k_{2} e^{\left(-4 \, t\right)} + 3 \, \sin\left(3 \, t\right) \]
\end{exerciseAnswer}