equations (ODEs) is examined for type I and II hidden symmetries where the analysis of
hidden symmetries for point symmetries is extended to contact symmetries. Ones invariant
under the group associated with the ten-dimensional (maximal) Lie algebra may produce
type I hidden symmetries for two-parameter subgroups and type II hidden symmetries for
certain solvable non-Abelian three-parameter subgroups in the third-order ODEs when they …