Third-order ordinary differential equations y′′′ = f(x, y, y′, y″) with maximal symmetry group

Abstract

We present here, in compact form, the necessary and sufficient conditions for linearization of third-order ordinary differential equations y'''=f (x,y,y', y'') with maximal symmetry group via point transformation. A simple procedure to construct the point transformation using the isomorphism of the symmetry subalgebra sl(2, ℝ) is also presented. This subalgebra is the semi-simple part of the Levi-Decomposition for the 7-dimensional symmetry algebra.