A lie symmetry approach for a non-linear ordinary differential equation arising in engineering sciences

Abstract

A non-linear second order ODE has some applications in engineering problems. In physics, it arises in the modeling of the flux of a heated compressible fluid through a long slender tube. In this paper, we consider a non-linear second order differential equation whose analytic solution cannot be obtained directly. Therefore, we first find the canonical transformations to rewrite the equation in terms of canonical variables by using the Lie symmetry approach. We then reduce the order of the equation, which is a first type Abel equation, to one by defining a new variable.