0000.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 0 = {x} + {x'} + 4 \, {y} \hspace{2em}x(0)= 5 \]\[ -{x} + 2 \, {y} = {y'} \hspace{2em}x(0)= 0 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= e^{\left(3 \, t\right)} + 4 \, e^{\left(-2 \, t\right)} \]\[y= -e^{\left(3 \, t\right)} + e^{\left(-2 \, t\right)} \]
\end{exerciseAnswer}