0002.tex

\begin{exerciseStatement}


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

\[ {y''} = -16 \, t e^{\left(3 \, t\right)} + {y} - 12 \, e^{\left(3 \, t\right)} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = -2 \, t e^{\left(3 \, t\right)} + k_{2} e^{\left(-t\right)} + k_{1} e^{t} \]
\end{exerciseAnswer}