Find this general solution:

y" + 3y' + 2y = 36xe^x

Here's my work:

1. r^2 + 3r + 2 = 0; r=-1, -2

2. yc = c1e^-x + c2^e^-2x

3. yp=Axe^x

y'p=Axe^x + Ae^x

y"p=Axe^x + 2Ae^x

4. (Axe^x + 2Ae^x) + 3(Axe^x + Ae^x) +2(Axe^x) = 36xe^x

5. 6Axe^x + 5Ae^x = 36xe^x

And here's where I get fuzzy. I need to find this value of A and then put in the form y = yc + yp. The answer in the back of the book is:

y= c1e^-x + c2^e^-2x + (6x-5)e^x

Any suggestions? Thanks, JN