(x2 - y2) = (x-y)* (x+y) and then (dx -dy)/(x-y)(x+y)=du/(x+y)u.

simplify (x+y) in the left side with (x+y) in the right side

Then (dx -dy)/(x-y) = du/u.

=> d(x-y)/(x-y) = du/u.

Integrating => ln(x-y) = ln U + ln C

=> ln[(x-y)/u] = ln C

=>(x-y)/u = c