MEMO 2008 T1

Determine all functions $f: \mathbb{R} \mapsto \mathbb{R}$ such that $x f(x + xy) = x f(x) + f \left( x^2 \right) f(y) \forall x,y \in \mathbb{R}.$

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.