Question 66
Find all functions $f : \mathbb{R} \to \mathbb{R}$, bounded in the interval $(0, 1)$ and such that
$$
x^2 f(x) - y^2 f(y) = (x^2 - y^2) f(x + y) - xy f(x - y)
$$
for all $x, y \in \mathbb{R}$.
$$
x^2 f(x) - y^2 f(y) = (x^2 - y^2) f(x + y) - xy f(x - y)
$$
for all $x, y \in \mathbb{R}$.