How to obtain singular integral of ordinary differential equations

Question

Consider the following nonlinear ODE

$$(xy^{\prime}-y)^{2}=x^{2}(x^{2}-y^{2})$$

find singular integral of this ODE.

I got its general solution by substituting $y=vx$ which is $\log(x)=\sin^{-1}(x)+c$.
How to get singular integral ?
Whether singular integral mean singular solution ?
How to apply c-discriminate?
Am I on right track ?
Please help to solve this example.

Answer 1

Applying $p$ dicriminent $$4x^2y^2-4(x^2y^2+x^4y^2+4x^6)=0$$ $$y=x$$ which the singular solution