Symmetry analysis of differential equations using MATHLIE

This article discusses a general procedure to solve ordinary differential equations of arbitrary order. The method used is based on symmetries of differential equation. The known symmetries allow the derivation of first integrals of the equation. The knowledge of at least $r$ symmetries of an ordinary differential equation of order $n$ with $r\ge n$ is the basis for deriving the solution. Our aim is to show that Lie's theory is instrumental for solving an ordinary differential equation of higher-order.