Solving Ordinary Differential Equations Using Lie Group

Abstract

This study is concerned about symmentries of differential equations. Symmetries are transformations leaving the set of solution invariant.suchtransformations are called point trnsformations . In the study, several differential equations were solved by changing to polar coordinates (r, θ). Also linearized symmetry condition for first order differential equations were considered.The study pointed out that , there are numerous possibilties for using symetry methods to solve higher order differential equations that has the symmetry form ( x ̂ , y ̂ ) = ( x,y+ λ) The symmetry condition reduce it to : ω (x,y) = ω(x,y+ λ).