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

Theorem
The first order ordinary differential equation:


 * $(1): \quad \left({x + y}\right) \mathrm d x = \left({x - y}\right) \mathrm d y$

is a homogeneous differential equation with solution:


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