MathDB
f(1) <=4/3 if (1+f(x))f''(x)=1+x , f(0)=1 , f'(0)=0

Source: 1976 Swedish Mathematical Competition p5

March 26, 2021
analysisinequalitiesfunctionalgebra

Problem Statement

f(x)f(x) is defined for x≥0x \geq 0 and has a continuous derivative. It satisfies f(0)=1f(0)=1, f′(0)=0f'(0)=0 and (1+f(x))f′′(x)=1+x(1+f(x))f''(x)=1+x. Show that ff is increasing and that f(1)≤4/3f(1) \leq 4/3.
Back to ProblemsView on AoPS