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

  • L. V. Ovsyannikov


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.

equivalence admissible operators invariant extension 


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  1. 1.
    S. Lie, “Classification und integration von gewöhnlichen differential-gleichungen zwischen x, y, die gruppe von transformationen gestatten,” Arch. Math. Natur. Christiania, 9, 371-393 (1883).Google Scholar
  2. 2.
    L. V. Ovsiannikov, Group Analysis of Differential Equations, Academic Press, New York (1982).Google Scholar

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

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