The question reads: Find the general solution to:

[(x^2)/2]y'' + 2xy' - (7/8)y = (x^4)/2 x>0

The first line on the solution sheet reads:

Characteristic eq: (1/2)r(r-1) + 2r - (7/8) = 0

I understand the substituting r for y's, but I don't see how he was able to get rid of the x's and get the r(r-1) part.

It would help a ton if someone could explain this to me.

Thanks a lot in advance.