First integrals and reduction of a class of nonlinear higher order ordinary differential equations

We propose a method for constructing first integrals of higher order ordinary differential equations. In particular third, fourth and fifth order equations of the form x(n) = h(x, x(n−1)) ˙x are considered. The relation of the proposed method to local and nonlocal symmetries are discussed.  2003 Published by Elsevier Inc.