RIOPLATENSE 2019 Problem 2

Find all functions $f:\mathbb{R}\rightarrow \mathbb{R}$ such that $f(f(x)^2+f(y^2))=(x-y)f(x-f(y))$

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.