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Ordinary Differential Equations

  • George W. Bluman
  • Sukeyuki Kumei
Part of the Applied Mathematical Sciences book series (AMS, volume 81)

Abstract

In this chapter we apply infinitesimal transformations (Lie groups of transformations) to the study of an nth order ordinary differential equation (ODE) written in a solved form
$${y_n} = f\left( {x,y,{y_1}, \ldots {y_n} - 1} \right),$$
(3.1)
where
$${y_k} = \frac{{{d^k}y}}{{d{x^k}}},k = 1,2,...,n.$$
ODE (3.1) defines a surface in (x,y,y1,...,y n )-space.

Keywords

Ordinary Differential Equation General Solution Solution Curve Infinitesimal Generator Invariant Curve 
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 Science+Business Media New York 1989

Authors and Affiliations

  • George W. Bluman
    • 1
  • Sukeyuki Kumei
    • 2
  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Faculty of Textile Science and TechnologyShinshu UniversityUeda, Nagano 386Japan

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