Journal of Applied Mechanics and Technical Physics

, Volume 45, Issue 2, pp 153–157

Group Classification of Equations of the Form y″ = f(x,y)

  • L. V. Ovsyannikov
Article

DOI: 10.1023/B:JAMT.0000017576.56850.8d

Cite this article as:
Ovsyannikov, L.V. Journal of Applied Mechanics and Technical Physics (2004) 45: 153. doi:10.1023/B:JAMT.0000017576.56850.8d

Abstract

The problem of classification of ordinary differential equations of the form y″ = f(x,y) by admissible local Lie groups of transformations is solved. “Standard” equations are listed on the basis of the equivalence concept. The classes of equations admitting a one‐parameter group and obtained from the “standard” equations by invariant extension are described.

equivalenceadmissible operatorsinvariant extension

Copyright information

© Plenum Publishing Corporation 2004

Authors and Affiliations

  • L. V. Ovsyannikov
    • 1
  1. 1.Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of SciencesNovosibirsk