# IF (x-y)f(x+y)-(x+y)f(x-y)=4xy(x+y)(x-y)for all x,y find f(x).

Sourabh Singh IIT Patna
5 years ago
mycroft holmes
272 Points
5 years ago
Let a = (x+y), b = (x-y) then $x = \frac{a+b}{2}, y = \frac{a-b}{2}$

Then the equation can be written as
b f(a) – a f(b) = ab (a2-b2).
Setting b = 1, we get f(a) – a f(1) = a3-a
Let f(1) = k, then f(a) = a3+(k-1)a