Problem

Source: Iranian third round 2018 algebra exam problem 2

Tags: algebra, functional equation



Find all functions $f: \mathbb{R}^{\ge 0} \to \mathbb{R}^{\ge 0}$ such that: $f(x^3+xf(xy))=f(xy)+x^2f(x+y) \forall x,y \in \mathbb{R}^{\ge 0}$