0000.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 2 \, {x} + {x'} = -3 \, {y} \hspace{2em}x(0)= 4 \]\[ -3 \, {y} + {y'} = -12 \, {x} \hspace{2em}x(0)= 1 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= e^{\left(7 \, t\right)} + 3 \, e^{\left(-6 \, t\right)} \]\[y= -3 \, e^{\left(7 \, t\right)} + 4 \, e^{\left(-6 \, t\right)} \]
\end{exerciseAnswer}