## general solution of ode using fourier transform

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..