System of ODEs

[tandoorichicken]

The problem goes like this:

"Show that $x = \sin(2t) + e^t, y = 2\cos(2t) - 4e^t$ is a solution of
$$x' = 5e^t + y, y' = -4x$$
and find a family of solutions of this system.

I already did the 'showing' part. I am having trouble finding the general solution for this system. Can someone help me?

 

[OlderDan]

Have you looked at the second derivative of x?