Solving Linear Differential Equations: A Novel Approach

2012/05/02 by N. Gurappa, Gurappa, N., Abhijit Sen +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1205.0385

openalex publication_date 2012/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that of the solutions are made transparent. We demonstrate the efficacy of the method by showing the common structure of the solution space of a wide variety of differential equations viz. Hermite, Laguerre, Jocobi, Bessel and hypergeometric etc. We also illustrate the use of the procedure to develop approximate solutions, as well as in finding solutions of many particle interacting systems.

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