MathNet 2022-part-02 — 197 problems (EN–VI) Question 25

A function $f: \mathbb{R} \to \mathbb{R}$ satisfies for all real $x$ and $y$ the equation $2f(x)(f(y))^2 + y^2f(-x|y|) = f(xy^2)$. Find all possible values of $f(1)$.