First Order ODE in form y' = F ((a x + b y + c) over (d x + e y + f))/Example

Theorem

$\dfrac {\d y} {\d x} = \dfrac {x + y + 4} {x - y - 6}$

The first order ODE:

$(1): \quad \dfrac {\d y} {\d x} = \dfrac {x + y + 4} {x - y - 6}$

has the general solution:

$\map \arctan {\dfrac {y + 5} {x - 1} } = \ln \sqrt {\paren {x - 1}^2 + \paren {y + 5}^2} + C$