PL-OM 1990 Problem 1

Find all functions $f : \mathbb{R} \longrightarrow \mathbb{R}$ that satisfy $(x - y)f(x + y) - (x + y)f(x - y) = 4xy(x^2 - y^2)$

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.