First Order ODE/y dx + (x^2 y - x) dy = 0/Proof 2

Proof
Rearranging, we have:
 * $x^2 y \, \mathrm d y - \left({x \, \mathrm d y - y \, \mathrm d x}\right) = 0$

Aiming to use Quotient Rule for Differentials, divide by $x^2$:
 * $y \, \mathrm d y = \dfrac{x \, \mathrm d y - y \, \mathrm d x} {x^2}$

So from Quotient Rule for Differentials: Formulation 1
 * $y \, \mathrm d y = \mathrm d \left({\dfrac y x}\right)$

from which the solution immediately drops:
 * $\dfrac {y^2} 2 - \dfrac y x = C$