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|f'(x)| <= C |f(x)|

Source: 1975 Swedish Mathematical Competition p6

March 26, 2021
algebraanalysis

Problem Statement

f(x)f(x) is defined for 0≤x≤10 \leq x \leq 1 and has a continuous derivative satisfying ∣f′(x)∣≤C∣f(x)∣|f'(x)| \leq C|f(x)| for some positive constant CC. Show that if f(0)=0f(0) = 0, then f(x)=0f(x)=0 for the entire interval.
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