Ordinary differential equations

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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 −...

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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...

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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...

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ژورنال

عنوان ژورنال: Journal of the Australian Mathematical Society

سال: 1977

ISSN: 1446-7887,1446-8107

DOI: 10.1017/s1446788700020024