, Volume 45, Issue 2, pp 153-157

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

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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.