BALKAN-SL 2007 A5

find all the function $f,g:R\rightarrow R$ such that (1)for every $x,y\in R$ we have $f(xg(y+1))+y=xf(y)+f(x+g(y))$ (2) $f(0)+g(0)=0$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.