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

Tohru Morita and Ken-ichi Sato
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Tohru Morita: Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan
Ken-ichi Sato: College of Engineering, Nihon University, Koriyama 963-8642, Japan

Mathematics, 2017, vol. 5, issue 4, 1-24

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.

Keywords: Green’s function; distribution theory; particular solution; Kummer’s differential equation; hypergeometric differential equation; Laplace transform (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2017
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