%0 Journal Article
%A Campoamor Stursberg, Otto-Rudwig
%T Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations
%D 2016
%@ 2073-8994
%U https://hdl.handle.net/20.500.14352/23854
%X A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.
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