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Research Article Open access CC BY 4.0

Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Nonstandard Analysis

Tohru Morita

Journal of Advances in Mathematics and Computer Science · pp. 49–60 · Published 21 Feb 2023

10.9734/jamcs/2023/v38i31751

Abstract

Discussions are presented by Morita and Sato on the problem of obtaining the particular solution of an inhomogeneous differential equation with polynomial coefficients in terms of the Green's function. In the present paper, solution is given without using the Green's function, on the basis of nonstandard analysis. It is applied to the hypergeometric, the Hermite, a simple ordinary and a fractional differential equation.

Differential equations with polynomial coefficients nonstandard analysis hypergeometric differential equation fractional differential equation Hermite differential equation

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