OME 2012 Problem 2

Find all functions $f:\mathbb{R}\to\mathbb{R}$ such that $(x-2)f(y)+f(y+2f(x))=f(x+yf(x))$ for all $x,y\in\mathbb{R}$ .

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.