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The functional equation problem of MEMO 2011 (team compt.)

Source: Middle European Mathematical Olympiad 2011 - Team Compt. T-1

September 6, 2011
functionalgebra proposedalgebra

Problem Statement

Find all functions f:R→Rf : \mathbb R \to \mathbb R such that the equality y2f(x)+x2f(y)+xy=xyf(x+y)+x2+y2y^2f(x) + x^2f(y) + xy = xyf(x + y) + x^2 + y^2 holds for all x,y∈Rx, y \in \Bbb R, where R\Bbb R is the set of real numbers.
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