Consider $f: R^+ \rightarrow R$ be differentiable and satisfy
$$f(y) - f(x) = \frac{x^x}{y^y} f\left(\frac{y^y}{x^x} \right)$$ for all x, y > 0. And $f^{'}(1) = 1$.
I need to find f(x). I tried differentiating both sides with respect to x but was not able to reach to the conclusion. Can I get a hint to approach this question? And what would be the line of thinking for such problems?
2026-04-01 17:22:37.1775064157
Functional Equation from BMT 2020
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