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yf(2x) - xf(2y) = 8xy(x^2 - y^2)

Source: Switzerland - 2006 Swiss MO Final Round p1

December 26, 2022
functionalfunctional equationalgebra

Problem Statement

Find all functions f:R→Rf : R \to R such that for all x,y∈Rx, y \in R holds yf(2x)−xf(2y)=8xy(x2−y2).yf(2x) - xf(2y) = 8xy(x^2 - y^2).
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