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

$y - x = 5 \, \map \ln {x + y - 1} + C$