Integrals of multinomial systems of ordinary differential equations

Ordinary Differential Equations and Singular Integrals

We present an informal review of some concepts and results from the theory of ordinary differential equations in the non-smooth context, following the approach based on quantitative a priori estimates introduced in [6] and [5].

An Algorithm for Determining Polynomial First Integrals of Autonomous Systems of Ordinary Differential Equations

be a system of n autonomous differential equations of first order . The co, are assumed to be polynomials in x . In addition they may contain one or more parameters Ck which are denoted collectively as c = (c l , c2 . . . . ) . One of the most prominent features governing the solution set of the autonomous system (1) is the chaotic behaviour which may occur in some regions of the parameter spac...

Integrating factors and first integrals for ordinary differential equations

We show how to find all the integrating factors and corresponding first integrals for any system of Ordinary Differential Equations (ODEs). Integrating factors are shown to be all solutions of both the adjoint system of the linearised system of ordinary differential equations and a system that represents an extra adjoint-invariance condition. We present an explicit construction formula to find ...

Ordinary Differential Equations and Dynamical Systems

Ordinary Differential Equations and Dynamical Systems

This manuscript provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore we consider linear equations, the Floquet theorem, and the autonomous...