Find all functions $f, g$ that satisfy the functional equation $$ f(x)-f(y)= (x -y)g(\sqrt{xy}) \quad \forall\ x,y>0. $$
Find all function such that $f(x)-f(y) = (x -y)g(\sqrt{xy})$
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functional-equations
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1try it yourself – 2012-11-08
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0Try to obtain an equation that only involves $g$. – 2012-11-08
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0I do it and i have this equation: (x^2-1)g(x)-(y^2-1)g(y)=(x^2-y^2)g(xy).If F(x)=(x^2-1)g(x) then we have the equation: ((X^2)*(y^2)-1)(F(x)-F(y))=(x^2-y^2)F(xy). I can't find any solution.Can you help me? – 2012-11-09