Undetermined coefficients to find general solution to system

Hi,

I'm having a bit of trouble with a problem here.

The question is: Use the Method of undetermined coefficients to Find the general solution to th system:

dx/dt = y + e^t

dy/dt = -2x + 3y + 1

I've got the homogenous solution fine, however I'm having a bit of difficulty with the particular solution.

I used xp = [ ctwe^t + ue^t ] where w was [1,1]^T but i know this trial doesnt include the 1 term and is therefore incorrect.

Can someone let me know what I'm supposed to do as a trial solution in this case. It's not explained in my notes, and I've looked online but to no avail.

Thanks!

Mike