y''-2y'+2y=x+1, y(0) = 3, y'(0)=0

I haven't done this in some time, please help.

I know I need to find the homogenous solution and add it to a particular solution.

Homogenous:

So , then the homogenous solution is

Particular:

Let y = Ax + B, y'=A, y''=0

0 -2 (A) + 2(Ax+B) = x+1

A=1/2, B=1,

yh + yp =