Lie group symmetries for first order ODEs

Abstract

This paper is centred on solving differential equations by symmetry groups for first order ODEs and is in response to Starrett (2007). It also explores the possibility of averting the assumptions by Olver (2000) that, in practice finding the solutions of the linearized symmetry condition is usually a much more difficult problem than solving the original ODE but, by inspired guesswork or geometric intuition, it is possible to ascertain a particular solution of the linearized symmetry condition. In addition, there is the verification of the connection between prolongation and the linearized symmetry condition as used in solving first order ODEs.