IR-TST 2008 Problem 1

Find all functions $f: \mathbb R\longrightarrow \mathbb R$ such that for each $x,y\in\mathbb R$ : $f(xf(y)) + y + f(x) = f(x + f(y)) + yf(x)$

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.