Find the general solution of the linear equation , x^{2}u_{x + }y^{2}u_{y}= (x+y)u .

I found out the first constant C_{1}= x^{-1 }- y^{-1 },

using dx/x^{2 }= dy/y^{2}= du/(x+y)u. (1)

According to my book, the second constant C_{2}= (x -y)/u , using (dx -dy)/ (x^{2}-y^{2}) = du/(x+y)u.

I don't understand how did they derive (dx -dy)/(x^{2}- y^{2}) from equation (1)?

Can someone please help me out with this ?