Assuming a power series solution of the form

Show that

2(dy/dx) + xy = x

has general solution y(x) = 1 + Ae^[(−x^2)/4] where A is a constant.

I know I have to substitute y = a(0) + a(1) x + a(2) x^2 + ....

into the equation and then equate the powers of x on both sides. After that solve for the sequence a(n). but i don't seem to be getting what I should? If anyone could help me that would be brilliant! xxx