0007.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

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