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A Class of Non-Linear ODEs with Movable Algebraic Singularities

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Abstract

A class of non-linear second-order rational ODEs is studied to show that any movable singularity of a solution that can be reached along a finite length curve is an algebraic branch point. Some conditions need to be imposed on the equations including the existence of certain formal algebraic series solutions. An example is discussed demonstrating the degree of restriction for the parameters of the equation.

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  1. Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK

    Thomas Kecker

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  1. Thomas Kecker
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Correspondence to Thomas Kecker.

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Kecker, T. A Class of Non-Linear ODEs with Movable Algebraic Singularities. Comput. Methods Funct. Theory 12, 653–667 (2012). https://doi.org/10.1007/BF03321848

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  • DOI: https://doi.org/10.1007/BF03321848

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