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Mathematics 2017, 5(4), 62; https://doi.org/10.3390/math5040062

Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Terms of the Green’s Function

1
Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan
2
College of Engineering, Nihon University, Koriyama 963-8642, Japan
*
Author to whom correspondence should be addressed.
Received: 30 September 2017 / Revised: 31 October 2017 / Accepted: 6 November 2017 / Published: 10 November 2017
(This article belongs to the Special Issue Operators of Fractional Calculus and Their Applications)
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Abstract

The particular solutions of inhomogeneous differential equations with polynomial coefficients in terms of the Green’s function are obtained in the framework of distribution theory. In particular, discussions are given on Kummer’s and the hypergeometric differential equation. Related discussions are given on the particular solution of differential equations with constant coefficients, by the Laplace transform. View Full-Text
Keywords: Green’s function; distribution theory; particular solution; Kummer’s differential equation; hypergeometric differential equation; Laplace transform Green’s function; distribution theory; particular solution; Kummer’s differential equation; hypergeometric differential equation; Laplace transform
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Morita, T.; Sato, K.-I. Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Terms of the Green’s Function. Mathematics 2017, 5, 62.

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