0005.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ 0 = -{x''} - 3 \, {x} + 4 \, {x'} \hspace{2em}
           {x} (0)= 4 ,
           {x} '(0)= 10 \]
\item \[ -100 \, {y} = {y''} \hspace{2em}
           {y} (0)= 3 ,
           {y} '(0)= -30 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = 3 \, e^{\left(3 \, t\right)} + e^{t} \]\[ {y} = 3 \, \cos\left(10 \, t\right) - 3 \, \sin\left(10 \, t\right) \]
\end{exerciseAnswer}