MathDB
Putnam 1961 B6

Source: Putnam 1961

June 5, 2022
Putnamfunctiondifferential equationroots

Problem Statement

Consider the function y(x)y(x) satisfying the differential equation y=(1+x)yy'' = -(1+\sqrt{x})y with y(0)=1y(0)=1 and y(0)=0.y'(0)=0. Prove that y(x)y(x) vanishes exactly once on the interval 0< x< \pi \slash 2, and find a positive lower bound for the zero.