0003.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ {x'} - {x} - 4 \, {y} = 0 \hspace{2em}x(0)= 3 \]\[ 2 \, {y} = {x} - {y'} \hspace{2em}x(0)= 2 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= 4 \, e^{\left(2 \, t\right)} - e^{\left(-3 \, t\right)} \]\[y= e^{\left(2 \, t\right)} + e^{\left(-3 \, t\right)} \]
\end{exerciseAnswer}