Details:
Title  Equivalence of differential equations of order one  Author(s)  Christophe Jermann, L.X. Chau Ngo, K.A. Nguyen, Maarten H. van der Vlerk  Type  Article in Journal  Abstract  Abstract The notion of strict equivalence for order one differential equations of the form f ( y ' , y , z ) = 0 with coefficients in a finite extension K of C ( z ) is introduced. The equation gives rise to a curve X over K and a derivation D on its function field K ( X ) . Procedures are described for testing strict equivalence, strict equivalence to an autonomous equation, computing algebraic solutions and verifying the Painlevé property. These procedures use known algorithms for isomorphisms of curves over an algebraically closed field of characteristic zero, the Risch algorithm and computation of algebraic solutions. The most involved cases concern curves X of genus 0 or 1. This paper complements work of M. Matsuda and of G. Muntingh & M. van der Put.  Keywords  Ordinary differential equations, Algebraic curves, Local behavior of solutions, Normal forms, Painlevé property, Algebraic solutions  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S0747717114001096 
Language  English  Journal  Journal of Symbolic Computation  Volume  71  Number  0  Pages  47  59  Year  2015  Edition  0  Translation 
No  Refereed 
No 
