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

Table 6

The adjoint table for the symmetries (28).

Ad	𝑋1	𝑋2	𝑋3	𝑋4
𝑋1	𝑋1	𝑋2	𝑋3	𝑋4−𝜖𝑋1
𝑋2	𝑋1	𝑋2	𝑋3	𝑋4−𝜖𝑋2
𝑋3	𝑋1	𝑋2	𝑋3	𝑋4−𝜖𝑋3
𝑋4	𝑒^𝜖𝑋1	𝑒^𝜖𝑋2	𝑒^𝜖𝑋3	𝑋4