2025-01-082024-06-101973-4409https://hdl.handle.net/10784/34853This paper makes significant contributions to the study of a generalized form of the Duffing-type equation. We derive the generating operators of the optimal system associated with this equation, enabling us to characterize an implicit solution. Additionally, we present a complete classification of group symmetries and obtain the Lagrangian for the equation. Our results include the classification of the Lie algebra and the optimal system, providing a thorough understanding of the equation’s underlying structure. These contributions serve to enhance the current body of knowledge on the Duffing-type equation and provide useful insights for future research in this area.engCopyright © 2024 Springer. All rights reserved.info:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccessContinuous group of Lie symmetriesOptimal systemInvariant solutionLagrangianLie algebra representationAcceso abierto2025-01-08Londoño, OscarGarcía, DaniloLoaiza, GabrielAcevedo, Yeisson10.1007/s12215-024-01038-y