need help w/ differential equation

hi everyone, this might sound a bit funny but i need some help with a homework problem. its a second order nonlinear DE. This is what i got so far...

problem: xy'' -x(y')^2 = y'

what i have so far:

u=y' and du/dx=y''

du/dx - u^2 = (1/x)u

int[(1/u)-u]du = int[1/x]dx <-------------int[ ] means integrate inside

ln u - (1/2)u^2 = ln x +c

ok, now is what ive done so far correct? what do i do next?

 

It's too late for me to think this all the way through, but I did spot one possible mistake.

After you substitute in u and du/dx for y' and y'' you divide through by x. This operation is not allowed unless you have stated that x != 0. Otherwise you may just be dividing by zero.