On the Method of Differential Invariants for Solving Higher Order Ordinary Differential Equations

There are many routines developed for solving ordinary differential Equations (ODEs) of different types. In the case an nth-order ODE that admits r-parameter Lie group (3≤r≤n), there is a powerful method symmetry analysis by which reduced to (n−r)th-order plus r quadratures provided algebra formed infinitesimal generators solvable. It would seem this not widely appreciated and/or used as it mentioned in related articles centred around integration higher order ODEs. interest mainstreaming method, we describe detail and provide four illustrative examples. We use third-order three-dimensional solvable present gist algorithm.