0007.tex

\begin{exerciseStatement}


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

\[ 18 \, t e^{\left(3 \, t\right)} - {y''} + {y'} - 15 \, e^{\left(3 \, t\right)} = -12 \, {y} \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {y} = k_{2} e^{\left(4 \, t\right)} - 3 \, t e^{\left(3 \, t\right)} + k_{1} e^{\left(-3 \, t\right)} \]
\end{exerciseAnswer}