First Order ODE/(1 - x y) y' = y^2

Theorem
The first order ODE:
 * $(1): \quad \paren {1 - x y} y' = y^2$

has the general solution:
 * $x y = \ln y + C$

Proof
Let $(1)$ be rearranged as:

It can be seen that $(2)$ is a linear first order ODE in the form:
 * $\dfrac {\d x} {\d y} + \map P y x = \map Q y$

where:
 * $\map P y = \dfrac 1 y$
 * $\map Q y = \dfrac 1 {y^2}$

Thus:

Thus from Solution by Integrating Factor, $(2)$ can be rewritten as: