الفهرس 
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Abstract
The object of this thesis is to master the analytical methods used for solution of non linear ordinary differential equations (NLODE) and find new solutions. In this thesis we
investigate NLODE, having unattainable closed form solutions, especially NLODE of higher differential order. As these equations play an important role in the study of nonlinear physical phenomena and engineering applications, we decided to go through this field of
research. In most cases, these equations are solved numerically and in some cases the solutions are analytically derived, using various transformation methods as well as a wealth of other analytical methods.
from this work resulted a paper entitled ;
”Generalized extended method for solution of nonlinear diffusion equations”[I], Journal of
Engineering and Applied Science.60 (2014). This paper investigates five diffusion problems solutions using extended Lie symmetry transformation. The thesis contains five main
chapters described hereafter;
Chapter 1
This chapter contains an exhaustive panel of non linear ordinary differential equations
describing physical phenomena. This is followed by a presentation of different analytical
methods of solutions for non linear ordinary differential equations and a review of previous publications for each method.
Chapter 2
In this chapter we present the integrability of non linear differential equations the
different non local symmetry transformation methods and the new different linearization
methods;
• Linearization through a transformation of the variables,