Question 130
Determine all functions $f: \mathbb{R} \to \mathbb{R}$, integrable over any bounded interval, satisfying the condition
$$
\int_{x-y}^{x+y} f(t) \, dt = y(f(x+y) + f(x-y)), \quad \text{for all real numbers } x \text{ and } y.
$$
$$
\int_{x-y}^{x+y} f(t) \, dt = y(f(x+y) + f(x-y)), \quad \text{for all real numbers } x \text{ and } y.
$$