0002.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 25 \, {x} + {x''} = 0 \hspace{2em}
           {x} (0)= -5 ,
           {x} '(0)= -15 \]
\item \[ -3 \, {y} - 2 \, {y'} = -{y''} \hspace{2em}
           {y} (0)= -5 ,
           {y} '(0)= -3 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -5 \, \cos\left(5 \, t\right) - 3 \, \sin\left(5 \, t\right) \]\[ {y} = -2 \, e^{\left(3 \, t\right)} - 3 \, e^{\left(-t\right)} \]
\end{exerciseAnswer}