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Function equation in Taiwan TST

Source: 2023 Taiwan TST Round 2 Independent Study 1-A

April 5, 2023
function equationalgebraTaiwan TST

Problem Statement

Find all functions f:R→Rf : \mathbb{R} \to \mathbb{R}, such that f(xy+f(y))f(x)=x2f(y)+f(xy)f\left(xy+f(y)\right)f(x)=x^2f(y)+f(xy) for all x,y∈Rx,y \in \mathbb{R}
Proposed by chengbilly
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