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

Proof
Rearranging, we have:
 * $x^2 y \rd y - \paren {x \rd y - y \rd x} = 0$

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

So from Quotient Rule for Differentials: Formulation 1
 * $y \rd y = \map \d {\dfrac y x}$

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