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Below is my question. I think I'm thinking too hard about it. Can anyone please point me to the right direction:

Given two functions $f, g$ differentiable on $\mathbb{R}$ so that $f'g - fg' = 0$ (logically equivalent). Does there exists constant $c$ so that either $f = cg$ or $g = cf$ ?

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    The result is not obvious. It is not even true.2012-12-07

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