0004.tex

\begin{exerciseStatement}


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


\begin{enumerate}[(a)]
\item \[ {x''} - 2 \, {x'} = 3 \, {x} \hspace{2em}
           {x} (0)= -1 ,
           {x} '(0)= -19 \]
\item \[ 0 = -25 \, {y} - {y''} \hspace{2em}
           {y} (0)= -4 ,
           {y} '(0)= 5 \]
\end{enumerate}
    
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[ {x} = -5 \, e^{\left(3 \, t\right)} + 4 \, e^{\left(-t\right)} \]\[ {y} = -4 \, \cos\left(5 \, t\right) + \sin\left(5 \, t\right) \]
\end{exerciseAnswer}