Find the general solution of the linear equation , x2ux + y2uy = (x+y)u .

I found out the first constant C1 = x-1 - y-1 ,

using dx/x2 = dy/y2 = du/(x+y)u. (1)

According to my book, the second constant C2 = (x -y)/u , using (dx -dy)/ (x2-y2) = du/(x+y)u.

I don't understand how did they derive (dx -dy)/(x2 - y2) from equation (1)?

Can someone please help me out with this ?