0004.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

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