Question

Solve: $(x+y)(dx-dy)=dx+dy$

Answer 1

Given,

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

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

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

integrating on both sides, we get,

$y+c=x-2\ln |x+y+1|+y+1+c$

$2\ln |x+y+1|=x+1$