ok well i'm pretty much home and dry in this problem

the aim of this problem is to get the general solution for the ode below..

2u'' - xu' + u = 0 = g(x)

i started to solve it by rearranging the equation..

2u'' + u = xu'

apply fourier transform..

2F(u'') + u^ = g^

(-2k^2)u^ + u^ = g^

u^ [1- 2(k^2)] = g^

u^ = {1/ [1- 2(k^2)]}g^

the problem is, i cant find any of the them in the transform table..