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

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

Grade:11

2 Answers

Sourabh Singh IIT Patna
askIITians Faculty 2104 Points
7 years ago
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mycroft holmes
272 Points
7 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
 

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