On Reduction of Some Differential Equations using Symmetry Methods

Abstract

In this paper Lie group theory is used to reduce the order of ordinary differential equations. For an ordinary differential equation admitting one parameter Lie group symmetry, order of differential equation, in principle, can always be reduce by one. Ordinary differential equation admitting mutli parameter Solvable Lie symmetry,  the order can be reduced by cardinality of admitted symmetry group.Seperation of variables by canonical coordinates of admitted is also given.

Keywords: Lie group, infinitesimal transformations, vector algebra, admitted symmetry