0010.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

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