0011.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ -{x''} = 4 \, {x} \hspace{2em}
           {x} (0)= -4 ,
           {x} '(0)= 0 \]
\item \[ 2 \, {y} = -{y''} + 3 \, {y'} \hspace{2em}
           {y} (0)= -8 ,
           {y} '(0)= -13 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -4 \, \cos\left(2 \, t\right) \]\[ {y} = -5 \, e^{\left(2 \, t\right)} - 3 \, e^{t} \]
\end{exerciseAnswer}