nonlinear first order differential equation nonlinear

Question

I was solving for the equation of a curve and I arrived at the following differential equation. However I do not know how to solve it:

$\frac{dy}{dx}=\frac{-x+\sqrt{x^2+y^2}}{y}$

Answer 1

$$ ydy +xdx=dx \sqrt{x^2 +y^2} \to d (x^2+ y^2) =2 dx\sqrt{x^2+y^2}$$

Take $u=x^2+y^2$, then $ du = 2\sqrt{u} dx$.