The solution of the differential equation (x+y)(d x-d y)=d x+d y, is

We have,

$(x+y)(d x-d y)=d x+d y$

$\Rightarrow d x-d y=\frac{d x+d y}{x+y}$

$\Rightarrow d(x-y)=\frac{d(x+y)}{x+y}$

$\Rightarrow x-y=\log (x+y)+\log C$                 [On integrating]

$\Rightarrow c(x+y)=e^{x-y}$

$\Rightarrow x+y=k e^{x-y}$, where $k=\frac{1}{C}$