λ-Symmetry and Integrating Factor For x ̈(f(t,x)+g(t,x)x ̇)e^x

Abstract

In this paper, we will calculate an integrating factor, first integral, and reduce the order of the non-Linear second-order ODEs , through the λ-symmetry method. Moreover, we compute an integrating factor, first integral and reduce the order for particular cases of this equation.