Second order non homogeneous diff. equation at constant coefficients

Hi there. I had some trouble trying to solve this:

(1)

At first I just found the solution for the homogeneous equation:

Then

So I've tried to find the particular solution. I thought I should suggest an equation like:

But then, when I've tried to find the undetermined coefficients for coefficients replacing in (1):

Then A=0,B=0,C=0 and D=-1.

So the general solution should be

But with wolfram alpha I've corroborated my solution is wrong: y''+y=cos(x)+3 sin(2x) - Wolfram|Alpha

So, where is the mistake and how should I do this?

I think I've found unless one mistake, just noted it. I should use instead of , because the first two terms are linearly dependent with the homogeneous solution, right?