Some tip you can share to solve this equation?

[GodsmacK]

Hi everyone,
I've been trying to solve the following equation:

$x^2(yy''-{y'}^2)+xyy'-y\sqrt{y^2+x^2y'^2}=0$

One of the tries was to do the substitution $z=xy'$. However, it doesn't seem to work...

 

[Chestermiller]

Try starting by dividing the equation by y², and working with z =y'/y. This will reduce it to a first order equation in z.

Chet