Finite Series of Distributional Solutions for Certain Linear Differential Equations

Abstract

In this paper, we present the distributional solutions of the modified spherical Bessel differential equations t2y′′(t)+2ty′(t)−[t2+ν(ν+1)]y(t)=0 and the linear differential equations of the forms t2y′′(t)+3ty′(t)−(t2+ν2−1)y(t)=0, where ν∈N∪{0} and t∈R. We find that the distributional solutions, in the form of a finite series of the Dirac delta function and its derivatives, depend on the values of ν. The results of several examples are also presented.

Generalized Solutions of Ordinary Differential Equations Related to the Chebyshev Polynomial of the Second Kind

“…where a, b, and c ∈ Z and t ∈ R. The authors studied the type of solution in the space of right-sided distributions, and they found that it depended on the values of a, b, and c. In 2020, Waiyaworn et al [15] studied the distributional solutions of linear ODEs of the forms…”