Invariant characterization of scalar third-order ODEs that admit the maximal point symmetry Lie algebra

Abstract

The Cartan equivalence method is used to deduce an invariant characterization of the scalar third-order ordinary differential equation u"' = f(x, u, u', u"), which admits the maximal 7-dimensional point symmetry Lie algebra. The method provides auxiliary functions that can be used to efficiently obtain the point transformation that does the reduction to the simplest linear equation u"' = 0. Moreover, examples are given to illustrate the method. Copyright ? 2018 John Wiley & Sons, Ltd.