0003.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 0 = {x''} + 4 \, {x} \hspace{2em}
           {x} (0)= 3 ,
           {x} '(0)= -8 \]
\item \[ 7 \, {y'} = {y''} + 10 \, {y} \hspace{2em}
           {y} (0)= -3 ,
           {y} '(0)= -3 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = 3 \, \cos\left(2 \, t\right) - 4 \, \sin\left(2 \, t\right) \]\[ {y} = e^{\left(5 \, t\right)} - 4 \, e^{\left(2 \, t\right)} \]
\end{exerciseAnswer}