0002.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 4 \, {x} + {x'} = 2 \, {y} \hspace{2em}x(0)= 1 \]\[ 0 = -{y'} - 2 \, {x} - 9 \, {y} \hspace{2em}x(0)= 1 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= 2 \, e^{\left(-5 \, t\right)} - e^{\left(-8 \, t\right)} \]\[y= -e^{\left(-5 \, t\right)} + 2 \, e^{\left(-8 \, t\right)} \]
\end{exerciseAnswer}