Real analysis: how to identify the family of functions of a given property.

A = {$ f: R a R $}

with the following properties

f has derivative of each order

$ for all x, y in R $ $ f (x + y) -f (y-x) = 2xf & # 39; (y) $

so I have to find the whole family

So far I can only show $ f (x) -f (-x) / 2x = 2xf & # 39; (0) $

I wanted to solve this problem.

Please provide only clue …

Thanks in advance