Sage Package for Symbolic Computation of Series Solution of Ordinary Differential Equations

The ordinary linear differential equations with constant coefficients can be solved by the algebraic methods and the solutions are obtained by elementary functions called the fundamental solutions. Most of the differential equations met in mathematics, physics and engineering sciences remain out of this class. In such cases, it is natural to search the solutions in the form of infinite series. The power series method is a well known procedure to solve ODEs with variable coefficients. The resulting series can be used to analyze and visualize the nature of the solutions of ODE’s for which direct calculation is difficult. Manually solving a series solution using power series method is tedious and time consuming. In this paper a special package using SAGE (an open source software) have been developed, which can calculate any number of coefficients with no restriction to obtain the series solutions of up to third order ODE at an ordinary point. Also the well known Legendre and Hermite polynomials of any order can be generated and visualized by the way getting series solutions, In addition, Frobenius method for finding series solution around regular singular point cases are discussed