Lie Point Algebraic Classification Of Linear Third Order Odes Using Differential Invariants

We obtain equivalence transformations for general linear third order ordinary differential equation (ODE) using Lie infinitesimal method. These equivalence transformations are then employed to deduce associated invariants. Derived invariants are used to reduce the linear third order ODEs with variable coefficients to simpler equations of this family with constant coefficients. It is shown that these reductions help in identifying the canonical forms of the linear third order ODEs with 4, 5, and 7-dimensional Lie point symmetry algebras. Though this algebraic classification for linear third order ODEs has already been presented, here differential invariants are shown to provide an alternate procedure to recover the same. We provide MAPLE codes used to derive the said invariants.