Distributional solutions of nth-order differential equations of the Bessel equation

Abstract

In this paper, we study the distributional solutions of nth-order differential equation of the form x²y⁽ⁿ⁾ (x)+xy^(n-1) (x)+(b²x²-p²)y^(n-2) (x) = 0 where p ≥ 0, n ≥ 2, b > 0 and x is a real variable. These solutions are obtained in the form of infinite series of the Dirac delta functions and its derivatives. We employ these solutions to observe their interesting features.