Method of characteristics and general solution for partial differential equations

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 ?

Re: Method of characteristics and general solution for partial differential equations

(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