MathDB

11.8

Part of 2007 Moldova National Olympiad

Problems(1)

Moldova NMO, 11th grade, Day 2, Problem 8

Source:

3/4/2007
The continuous function and twice differentiable function f:R→Rf: \mathbb{R}\rightarrow\mathbb{R} satisfies 20072⋅f(x)+f′′(x)=02007^{2}\cdot f(x)+f''(x)=0. Prove that there exist two such real numbers kk and ll such that f(x)=l⋅sin⁡(2007x)+k⋅cos⁡(2007x)f(x)=l\cdot\sin(2007x)+k\cdot\cos(2007x).
functioncalculusderivativereal analysisreal analysis unsolved