Journal of Applied Mechanics and Technical Physics

, Volume 45, Issue 2, pp 153-157

First online:

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

  • L. V. OvsyannikovAffiliated withLavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences

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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