Ordinary Differential Equations

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


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
$${y_n} = f\left( {x,y,{y_1}, \ldots {y_n} - 1} \right),$$
$${y_k} = \frac{{{d^k}y}}{{d{x^k}}},k = 1,2,...,n.$$
ODE (3.1) defines a surface in (x,y,y1,...,y n )-space.


Ordinary Differential Equation General Solution Solution Curve Infinitesimal Generator Invariant Curve 
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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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