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.
Highlights
In our recent papers [1,2], we are concerned with the solution of Kummer’s and hypergeometric differential equations, where complementary solutions expressed by the confluent hypergeometric series and the hypergeometric series, respectively, are obtained, by using the Laplace transform, its analytic continuation, distribution theory and the fractional calculus
It is the purpose of the present paper, to give the formulas which give the particular solutions of those equations with inhomogeneous term in terms of the Green’s function
We present the solutions giving particular solutions of Kummer’s and the hypergeometric differential equation in terms of the Green’s function with the aid of distribution theory
Summary
In our recent papers [1,2], we are concerned with the solution of Kummer’s and hypergeometric differential equations, where complementary solutions expressed by the confluent hypergeometric series and the hypergeometric series, respectively, are obtained, by using the Laplace transform, its analytic continuation, distribution theory and the fractional calculus It is the purpose of the present paper, to give the formulas which give the particular solutions of those equations with inhomogeneous term in terms of the Green’s function. We use them in giving the particular solution of differential equation with polynomial coefficients in terms of the Green’s function, and the solutions are obtained by this method for Kummer’s and the hypergeometric differential equation in Sections 4 and 5, respectively.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
