0009.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 0 = -{x''} - 81 \, {x} \hspace{2em}
           {x} (0)= -3 ,
           {x} '(0)= -45 \]
\item \[ -20 \, {y} + {y'} = -{y''} \hspace{2em}
           {y} (0)= -3 ,
           {y} '(0)= -12 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -3 \, \cos\left(9 \, t\right) - 5 \, \sin\left(9 \, t\right) \]\[ {y} = -3 \, e^{\left(4 \, t\right)} \]
\end{exerciseAnswer}