On the Oscillations of Second Order Linear Differential Equations

Abstract

This paper extends the discriminant associated to second order linear constant coefficient differential equations to general second order linear differential equations. The main result of this paper is that the discriminant of a second order linear differential equation is a function who bounded behaviour determines whether solutions oscillate on an infinite interval, i.e. has infinitely many zeroes. This paper is accessible to any undergraduate who has completed a course in differential equations, and basic analysis.