0000.tex

\begin{exerciseStatement}


Explain how to find the particular solution to each given IVP.


\begin{enumerate}[(a)]
\item \[ -{x''} - 4 \, {x} = 0 \hspace{2em}
           {x} (0)= 1 ,
           {x} '(0)= 8 \]
\item \[ -{y''} - 12 \, {y} = 7 \, {y'} \hspace{2em}
           {y} (0)= -1 ,
           {y} '(0)= 2 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = \cos\left(2 \, t\right) + 4 \, \sin\left(2 \, t\right) \]\[ {y} = -2 \, e^{\left(-3 \, t\right)} + e^{\left(-4 \, t\right)} \]
\end{exerciseAnswer}