Linearization Problem for Third-Order ODEs with Four- and Five-Dimensional Lie Symmetry Algebras under Contact Transformations

Omar A. Abuloha; Marwan Aloqeili; Ahmad Y. Al-Dweik; F. M. Mahomed

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arXiv · 2605.06704

Linearization Problem for Third-Order ODEs with Four- and Five-Dimensional Lie Symmetry Algebras under Contact Transformations

Omar A. Abuloha·Marwan Aloqeili·Ahmad Y. Al-Dweik·F. M. Mahomed

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Abstract

Using Cartan equivalence method, invariant coframes are constructed for two branches of rank one and zero, which characterize linearizable third-order ODEs under contact transformations with four- and five-dimensional Lie symmetry algebras, respectively. A procedure for deriving the corresponding contact transformations is also presented, along with illustrative examples.

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Omar A. Abuloha, Marwan Aloqeili, Ahmad Y. Al-Dweik, F. M. Mahomed. 2026-05-06. Linearization Problem for Third-Order ODEs with Four- and Five-Dimensional Lie Symmetry Algebras under Contact Transformations. https://arxiv.org/abs/2605.06704

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