¿How to solve this functional equation: $xf(y)+yf(x)=(x+y)f(x)f(y)$? Need some help!
Find all $f:\mathbb R\to\mathbb R$ such that $\forall x,y\in\mathbb R$ the given equality holds: $xf(y)+yf(x)=(x+y)f(x)f(y)$.