A class of non-linear ODEs with movable algebraic singularities

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A class of nonlinear second-order rational ODEs is studied for which it is shown 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.
Original languageEnglish
Pages (from-to)653-667
JournalComputational Methods and Function Theory
Issue number2
Publication statusPublished - 10 Dec 2012


  • movable singularities
  • solutions of ODEs


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