I was trying to solve this differential equation but can't figure out the final integral I get by variable separable method
The equation is $$ x^3 \, y' = y^3 + y^2 \, \sqrt{y^2-x^2} $$
I got the integral $$ \frac{dv}{v^3 + v^2 \sqrt{(v^2 - 1)} - v} $$ but can't figure out how to solve it.
The Euler substitution $v= \frac{u^2 + 1}{2u}$ could work but I can't seem to proceed with it.
Any help with this problem is much appreciated.