Question 95
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ such that the equality
$$
y^{2} f(x)+x^{2} f(y)+x y=x y f(x+y)+x^{2}+y^{2}
$$
holds for all $x, y \in \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers.
$$
y^{2} f(x)+x^{2} f(y)+x y=x y f(x+y)+x^{2}+y^{2}
$$
holds for all $x, y \in \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers.