Problem

Source: India IMOTC Practice Test 1 Problem 1

Tags: functional equation, algebra, IMOTC



Find all functions $f:\mathbb R \to \mathbb R$ such that \[ xf(xf(y)+yf(x))= x^2f(y)+yf(x)^2, \]for all real numbers $x,y$. Proposed by B.J. Venkatachala