Derivable function with reciprocal condition

1925SpecialistCalculusDifferential Equations

Olimpiada Republicană la Matematică

Determine all differentiable functions $F:(0 ;+\infty) \rightarrow \mathbb{R}$ such that $F(1)=1$ and $F\left(\frac{1}{x}\right) F^{\prime}(x)=\frac{1}{x} \ln x$.

0 students attempted0% solvedRating 1925

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Derivable function with reciprocal condition

1925SpecialistCalculusDifferential Equations

Olimpiada Republicană la Matematică

Determine all differentiable functions $F:(0 ;+\infty) \rightarrow \mathbb{R}$ such that $F(1)=1$ and $F\left(\frac{1}{x}\right) F^{\prime}(x)=\frac{1}{x} \ln x$.

0 students attempted0% solvedRating 1925