Characterization of Symmetry Properties of First Integrals for Submaximal Linearizable Third-Order ODEs

Table 1

The commutation relations for the symmetries of (1).

[𝑋𝑖, 𝑋𝑗]	𝑋1	𝑋2	𝑋3	𝑋4	𝑋5
𝑋1	0	0	𝑋3	−𝑋4	0
𝑋2	0	0	0	0	𝑋2
𝑋3	−𝑋3	0	0	0	𝑋3
𝑋4	𝑋4	0	0	0	𝑋4
𝑋5	0	−𝑋2	−𝑋3	0	0