Ordinary Differential Equations: Symmetry Generators

In this chapter, ordinary differential equations will be treated. There are two basic steps in finding solutions for ordinary differential equations via symmetry methods: 1) Calculate the symmetry generators 2) Use the generators to construct solutions. The first part, namely calculating the symmetries of the ODEs will be outlined in this chapter and the next chapter is devoted to constructing solutions from the generators. First order, second order and higher order differential equations will be treated separately. 4.1. EXTENDED GROUPS AND INFINITESIMAL GENERATORS A general nonlinear ordinary differential equation of k’th order