0005.tex

\begin{exerciseStatement}


Find the solution to the given system of IVPs.

\[ 2 \, {y} + {x} = -{x'} \hspace{2em}x(0)= 3 \]\[ {y'} + 6 \, {y} = 2 \, {x} \hspace{2em}x(0)= 3 \]
\end{exerciseStatement}
    
\begin{exerciseAnswer} 
\[x= 2 \, e^{\left(-2 \, t\right)} + e^{\left(-5 \, t\right)} \]\[y= e^{\left(-2 \, t\right)} + 2 \, e^{\left(-5 \, t\right)} \]
\end{exerciseAnswer}