Differential equations - undetermined coefficients

Hey guys!

I have a quiz tomorrow and i'm not going to be able to sleep unless I understand the solution to this question. it's long, I kinda feel bad even asking (Doh)

Anyway the question is:

Use method of undetermined coefficients to find the particular solution to

y''' - 3y'' + 4y = e^2x

I took my yp = x^2 * Ae^2x

I multipllied by x^2 because of the double roots ( I got 2,2,-1 for roots)

Thanks so much to anyone who can help me... I know its a long one.