Find the solution to the given system of IVPs.
\[ {x} = 2 \, {y} + {x'} \hspace{2em}x(0)= 3 \]
\[ -{y'} = -6 \, {y} - 2 \, {x} \hspace{2em}x(0)= -3 \]
Answer:
\[x= e^{\left(5 \, t\right)} + 2 \, e^{\left(2 \, t\right)} \]
\[y= -2 \, e^{\left(5 \, t\right)} - e^{\left(2 \, t\right)} \]