IZhO 2017 Problem 2

Find all functions $f:R \rightarrow R$ such that $(x+y^2)f(yf(x))=xyf(y^2+f(x))$ , where $x,y \in \mathbb{R}$

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.