Non exact differential equation, initial value problem

[Cocoleia]

Homework Statement

I am trying to solve the following:
y'''-9y'=54x-9-20e^2x with y(0)=8, y'(0)=5, y''(0)=38

Homework Equations

The Attempt at a Solution

The right answer is:
y= 2+2e^3x+2e^(-3x)-3x^2+x+2e^2x

I am only wrong on the coefficients C2 and C3. Where did I mess up in my solution?

 

[eys_physics]

When computing $y'$ at the top of the second you are missing the constant $1$ coming from $(x)'$=1.