Question 166
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that
$$
x[f(x+y)-f(x-y)]=4 y f(x)
$$
for any real numbers $x, y$.
$$
x[f(x+y)-f(x-y)]=4 y f(x)
$$
for any real numbers $x, y$.
MathNet 2016-part-04 — 184 problems (EN–VI) Question 166
Math Olympiad Vault · MathNet 2016-part-04 — 184 problems (EN–VI)