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A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution

L. G. S. Duarte·S. E. S. Duarte·L. A. C. P. da Mota
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Abstract

We present an algorithm to solve First Order Ordinary Differential Equations (FOODEs) extending the Prelle-Singer (PS) Method. The usual PS-approach miss many FOODEs presenting Liouvillian functions in the solution (LFOODEs). We point out why and propose an algorithm to solve a large class of these previously unsolved LFOODEs. Although our algorithm does not cover all the LFOODEs, it is an elegant extension mantaining the semi-decision nature of the usual PS-Method.

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L. G. S. Duarte, S. E. S. Duarte, L. A. C. P. da Mota. 2001-07-10. A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution. https://doi.org/10.1088/0305-4470%2F35%2F17%2F306

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