Elements of ordinary differential equations

Summary: Ordinary Differential Equations

1 Initial Value Problem We are given a right hand side function f(t, y) with f : [t0, T ]×Rn → Rn and an initial value y0 ∈ Rn. We want to find a function y(t) with y : [t0, T ] → Rn such that y′(t) exists, is continuous and satisfies the initial value problem y′(t) = f (t, y(t)) , y(t0) = y0. (1) We assume that f(t, y) satisfies a Lipschitz condition with respect to y (at least for y with |y −...

Linearizable ordinary differential equations . ∗

Our purpose in this paper is to study when a planar differential system polynomial in one variable linearizes in the sense that it has an inverse integrating factor which can be constructed by means of the solutions of linear differential equations. We give several families of differential systems which illustrate how the integrability of the system passes through the solutions of a linear diff...

Ordinary Differential Equations

Abstract We extend the Eruguin result exposed in the paper ”Construction of the whole set of ordinary differential equations with a given integral curve” published in 1952 and construct a differential system in R which admits a given set of the partial integrals, in particular we study the case when theses functions are polynomials. We construct a non-Darboux integrable planar polynomial system...

Nonlinear Ordinary Differential Equations

Most physical processes are modeled by differential equations. First order ordinary differential equations, also known as dynamical systems, arise in a wide range of applications, including population dynamics, mechanical systems, planetary motion, ecology, chemical diffusion, etc., etc. See [19, 72,ODES] for additional material and applications. The goal of this chapter is to study and solve i...

Ordinary Differential Equations