Details:
Title  Birational transformations preserving rational solutions of algebraic ordinary differential equations  Author(s)  L.X. Chau Ngo, J. Rafael Sendra, Franz Winkler  Type  Article in Journal  Abstract  Abstract We characterize the set of all rational transformations with the property of preserving the existence of rational solutions of algebraic ordinary differential equations (AODEs). This set is a group under composition and, by its action, partitions the set of AODEs into equivalence classes for which the existence of rational solutions is an invariant property. Moreover, we describe how the rational solutions, if any, of two different AODEs in the same class are related.  Keywords  Algebraic differential equation, Rational solution, Integral birational transformation, Integral curve, Rational parametrization  ISSN  03770427 
URL 
http://www.sciencedirect.com/science/article/pii/S0377042715001533 
Language  English  Journal  Journal of Computational and Applied Mathematics  Volume  286  Number  0  Pages  114  127  Year  2015  Edition  0  Translation 
No  Refereed 
No 
