Solution of Inhomogeneous Differential Equations with Polynomial Coefficients in Nonstandard Analysis
Tohru Morita *
Graduate School of Information Sciences, Tohoku University, Sendai 980-8577, Japan.
*Author to whom correspondence should be addressed.
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.
Keywords: Differential equations with polynomial coefficients, nonstandard analysis, hypergeometric differential equation, fractional differential equation, Hermite differential equation