We compute for the representative scalar ordinary differential equation of maximal point symmetry the generalised symmetries of order-one and two. We examine the Lie Brackets for the generalised symmetries and see that closure does not occur for generalised symmetries of order-two. Consequently all generalised symmetries up to the maximum order possible must be admitted.
Charalambous, K. and Leach, PGL
"Algebraic Structures of Generalised Symmetries of n th-order Scalar Ordinary Differential Equations of Maximal Lie Point Symmetry,"
Applied Mathematics & Information Sciences: Vol. 09:
3, Article 9.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/9