NL-BXMO-TST 2020 Problem 3

Find all functions $f: R \to R$ that satisfy $f (x^2y) + 2f (y^2) =(x^2 + f (y)) \cdot f (y)$ for all $x, y \in R$

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.