INRIA, Sophia Antipolis, France

Evelyne.Hubert@inria.fr

http://www-sop.inria.fr/cafe/Evelyne.Hubert

It is now well known that a system of *n* linear first order
ordinary differential equations is equivalent to a single differential
equation of order *n*. We shall expose a generalisation to
nonlinear differential systems.

A polynomial differential system is equivalent to a finite set of differentially triangular systems (or differential characteristic sets). This set can be computed effectively by recent algorithms based on differential algebra and implemented in Maple. We show that the solution set of such a differentially triangular system is birationnally equivalent to the general solution of a single differential equation. We give an algorithm to compute this equation and the expression of the equivalence.