Method of substitution in Differential Equation

Question

When solving the equation $(x^2+y^2)dx+(x^2-xy)dy=0$ you first identify it's an homogeneous equation. Using $y=ux$ equation is reduced to the separable equation $$\frac{dx}{x}=\frac{u-1}{u+1}du$$ If we use $x=vy$ we arrive to the equation $$\frac{dy}{y}+\frac{v^2+1}{v^3+v^2}dv=0$$ As you can see the first one is easier to integrate using long divition (though I know the second can be done using partial fractions). So my question is if there is a way to find out which is the best substitution to use. Zill in his book recommends using $x=vy$ when $M$ is simpler than $N$ in $Mdx+Ndy=0$, I tried this but it's not true