Problem

Source: XIII International Festival of Young Mathematicians Sozopol 2024, Theme for 10-12 grade

Tags: functional equation, algebra



Find all functions \( f: \mathbb{R}^{+} \to \mathbb{R}^{+} \) such that: \[ f(x^2 + y) = xf(x) + \frac{f(y^2)}{y} \] for any positive real numbers \( x \) and \( y \).