I did that and got to y'=(x/y)((1+(y/x)^2)^.5-1) and then used a substitution of v=y/x.
Reducing it to y'=(1/v)((1+v^2)^.5-1) and differentiating y=vx to get y'=v+x*dv/dx.
Setting up an integral of v/((1+v^2)^.5-1-v^2)*dv=dx/x But I have attempted many times with this integral and have not gotten the correct solution.
See here: integrate x/(Sqrt[x^2 + 1] - (x^2 + 1)) - Wolfram|Alpha (click on show steps).
The initial equation becomes