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**Let z(x,y)= 2x+ g(xy) and add the initial value conditon, z= x on the line y=1. Find the general solution of the initial value problem.**

1. Replace z(x,y)=2x+g(xy) wih the condition to get x= 2x+g(x) for all x, so that g(x)= -x

I understand everything so far but then the next step says "hence z(x,y)= 2x-xy is the general solution." Where does the -xy come from?

Any help or advice would be much appreciated! Thank you