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Putnam 1961 B6

  • Session B
  1. Consider the function y(x)y(x) satisfying the differential equation y′′=−y^{\prime \prime}=- (1+x)y(1+\sqrt{x}) y with y(0)=1y(0)=1 and y′(0)=0y^{\prime}(0)=0. Prove that y(x)y(x) vanishes exactly once on the interval 0<x<π/20<x<\pi / 2, and find a positive lower bound for the zero.

Dataset text PutnamGAP. Quoted with source.

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