Solution of differential equation (x-y)^2dy/dx=1 is:

$x - y = t$  $⇒1-\frac{dy}{dx}=\frac{dt}{dx}⇒1-\frac{dt}{dx}=\frac{1}{t^2}⇒\int dx=\int\frac{t^2}{t^2-1}dx$

$⇒y=\frac{1}{2}\log|\frac{t-1}{t+1}|=c⇒y=\frac{1}{2}\log|\frac{x-y-1}{x-y+1}|+c$