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

Theorem
The first order ODE:
 * $\left({x + y}\right) \mathrm d x = \left({x - y}\right) \mathrm d y$

has the solution:
 * $\arctan \dfrac y x = \ln \sqrt{x^2 + y^2} + C$

Proof
We have: