0001.tex

\begin{exerciseStatement}


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

\[ 0 = 36 \, t e^{\left(3 \, t\right)} + 3 \, {y} - {y''} - 2 \, {y'} + 24 \, e^{\left(3 \, t\right)} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = 3 \, t e^{\left(3 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} + k_{2} e^{t} \]
\end{exerciseAnswer}