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x [f(x + y) - f (x - y)] = 4y f (x)

Source: 2016 Saudi Arabia IMO TST , level 4, II p3

July 29, 2020
algebrafunctionalfunctional equation

Problem Statement

Find all functions f:R→Rf : R \to R such that x[f(x+y)−f(x−y)]=4yf(x)x[f(x + y) - f (x - y)] = 4y f (x) for any real numbers x,yx, y.
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