Differential Equations

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


In this chapter the first order differential equation
$$\frac{{dy}}{{dx}} = f(x,y)$$
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
$$dy = f(x,y)dx.$$


Uniqueness Theorem Integrability Condition Linear Differential Equation Lipschitz Condition Normal System 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1973

Authors and Affiliations

  1. 1.Department of Mathematics, UniversityHelsinkiFinland

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