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

Theorem
The first order ODE:
 * $(1): \quad y \, \mathrm d x + \left({x^2 y - x}\right) \mathrm d y = 0$

has the solution:
 * $\dfrac {y^2} 2 - \dfrac y x = C$

This can also be presented in the form:
 * $\dfrac {\mathrm d y} {\mathrm d x} + \dfrac y {x^2 y - x}$