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Differential Equations

Chapter
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Part of the Die Grundlehren der mathematischen Wissenschaften book series (GL, volume 102)

Abstract

In this chapter the first order differential equation
$$\frac{{dy}}{{dx}} = f(x,y)$$
(0.1)
is to be investigated. Here x is a vector in an m-dimensional linear space R x m , and y = y(x) is a vector function, which is to be determined The range of y lies in an n-dimensional space R y n , while f(x,y) stands for a linear operator, which maps the space R x m into the space R y n In differential form the equation is
$$dy = f(x,y)dx.$$
(0.1′)

Keywords

Uniqueness Theorem Integrability Condition Linear Differential Equation Lipschitz Condition Normal System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  1. 1.Department of Mathematics, UniversityHelsinkiFinland

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