Question 103
Find all functions $f : \mathbb{R} \to \mathbb{R}$ such that
$$
2f(x)f(x + y) - f(x^2) = \frac{x}{2}(f(2x) + 4f(f(y)))
$$
for all $x, y \in \mathbb{R}$.
$$
2f(x)f(x + y) - f(x^2) = \frac{x}{2}(f(2x) + 4f(f(y)))
$$
for all $x, y \in \mathbb{R}$.