0011.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ -4 \, {x} = -4 \, {y} - {x'} \hspace{2em}x(0)= 3 \]\[ -9 \, {x} - {y'} = {y} \hspace{2em}x(0)= 10 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= -e^{\left(8 \, t\right)} + 4 \, e^{\left(-5 \, t\right)} \]\[y= e^{\left(8 \, t\right)} + 9 \, e^{\left(-5 \, t\right)} \]
\end{exerciseAnswer}