Question 169
Find all functions $f: \mathbb{R} \to \mathbb{R}$, such that for any real $x$, $y$ holds the following:
$$
xf(x) + yf(xy) = xf(x + yf(y))
$$
$$
xf(x) + yf(xy) = xf(x + yf(y))
$$
MathNet 2023-part-06 — 191 problems (EN–VI) Question 169
Math Olympiad Vault · MathNet 2023-part-06 — 191 problems (EN–VI)