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An extensible differential equation solver

We describe a method for solving linear second order differential equations in terms of hypergeometric and other (less well known) special functions. Intended as a method for computer algebra systems, the solver described in this article uses a database of functions to construct an anstatz for the solution. A user may extend the solver by appending functions to the database. An overview of a Macsyma language implementation, with sample calculations, is given.