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

Theorem
The first order ordinary differential equation:


 * $(1): \quad \paren {x + y} \rd x = \paren {x - y} \rd y$

is a homogeneous differential equation with general solution:


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