Question: solve: 2x^2y'' + 5xy' + y = x^2 - x

My attempt so far: y'' + (5y'/2x) + (y/x^2) = 1/2 - 1/(2x)

yh: λ^2 + (5/2)λ +1 = 0

(2λ+1)(λ+2) = 0

λ = -1/2, -2

yh= c1e^(-1/2x) + c2e^(-2x)

Try yp = Ae^(-1/2x) + Bxe^(-1/2x) + C, but e^(-1/2x) is part of yh.

yp= Axe^(-1/2x) + Bx^2e^(-1/2x) + C

is this correct so far?