Question

Find the general solution of differential equation.

$dx-dy+ydx+xdy=0$.

Answer 1

$dx(1+y)-dy(1-x)=0$

$dx(1+y)=dy(1-x)$

$\frac{dx}{1-x}=\frac{dy}{1+y}$

$ln(1-x)=ln\left(c\right(1+y\left)\right)$ (where 'c' is constant)

$1-x=c(1+y)$

$x+cy+(c-1)=0$