Linearization Problem for a System of Two Second-Order ODEs via Cartan's Method: Branch I

2026/07/18 by Batoul M. Raddad, Ahmad Y. Al-Dweik, Marwan Aloqeili +1
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Abstract

Cartan's method classifies the class of linearizable system of two second-order ODEs into many branches. This paper investigates Branch I of the classification, characterized by a rank-one generalized Wilczynski invariant matrix and the vanishing of two relative invariants K₁ and L₁. It is demonstrated that any linearizable system belonging to this branch admits an eight-dimensional Lie point symmetry algebra. The canonical form for this class is provided and the invariant characterizations based on the obtained rank-zero invariant coframe and the corresponding constant structure equations are established. Also, a systematic procedure for constructing the linearizing point transformation is derived. The theoretical results are illustrated by several examples.

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