Second order linear nonhomogeneous equations

How do I find the general solution for the following equation?

y''-2/x^2 y= 3-x^-2; y1=x^2, y2=x^-1

i dunno lol

Like this: http://i32.tinypic.com/2dmd52.jpg

substitute y = x^2u
y' = 2xu + x^2 u'
y'' = 2u + 4x u' + x^2 u''

y''-2/x^2 y=  2u + 4x u' + x^2 u'' - 2u = 3- x^-2

4xu' + x^2u'' = 3 - x^-2

let u' = v

4xv + x^2v' = 3 - x^-2
4x^3v + x^4v' = 3x^2 - 1
x^4 * v = x^3 - x + A
v = u' = x^-1 - x^-3 + Ax^-4
u = log x + 1/2 x^-2 + A'x^-3 + B
y = x^2 u = x^2 log x + 1/2 + A/x + Bx^2

>>4
My way was faster.

Can anyone do it with variation parameters

This was the answer given by the book. http://i9.photobucket.com/albums/a92/onehundredpercent/answer.jpg