### International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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### Problem 4

Problem 4. Find all differentiable functions $\displaystyle f:(0,\infty)\to\RR$ such that

$\displaystyle f(b)-f(a)=(b-a)f'\left(\sqrt{ab}\right) \quad \text{for all} \quad a,b>0. \tag2$

(Proposed by Orif Ibrogimov, National University of Uzbekistan)

Hint: Differentiate the equation and transform it to a differential equation.