Does there exist any function $f: \mathbb{R}^+ \to \mathbb{R}$ such that for all positive real numbers $x,y$ the following is true : $$f(xf(x)+yf(y))=xy$$
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$x (f(x ) + f'(x)) = C$ – jonsno May 10 '17 at 14:50
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f need not be differentiable. If you claim it is differentiable please prove it. – Aditya Guha Roy May 10 '17 at 14:58
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1https://artofproblemsolving.com/community/c6h1445131 – Aditya Guha Roy May 22 '17 at 04:41