Solve the following differential equation: `x ylog(x/y)dx+{y^2-x^2log(x/y)}dy=0`

Explanation

Given , $$x y \log \left(\frac{x}{y}\right) d x +\left\{y^{2}-x^{2} \log \left(\frac{x}{y}\right)\right\} d y=0 $$
$$ \frac{d y}{d x}=\frac{x^{2} \log \left(\frac{x}{y}\right)-y^{2}}{x y \log \left(\frac{x}{y}\right)} $$
It is a homogeneous equation

...