0004.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ -{x'} - 4 \, {y} = {x} \hspace{2em}x(0)= -5 \]\[ -{y'} = -2 \, {y} + {x} \hspace{2em}x(0)= 0 \]
\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}