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.