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

Source:

March 4, 2007
functioncalculusderivativereal analysisreal analysis unsolved

Problem Statement

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).
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