Campoamor Stursberg, Otto-Rudwig2023-06-182023-06-182016-03-172073-899410.3390/sym8030015https://hdl.handle.net/20.500.14352/23854A 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.engAtribución 3.0 Españajournal articlehttps://doi.org/10.3390/sym8030015https://www.mdpi.com/2073-8994/8/3/15open access517.9512Lie systemsVessiot-Guldberg-Lie algebraSuperposition ruleSODE Lie systemsÁlgebraEcuaciones diferenciales1201 Álgebra1202.07 Ecuaciones en Diferencias