Thesis (M.Sc.)-University of Natal, Durban, 2000.The study of second order ordinary differential equations is vital given their proliferation in
mechanics. The group theoretic approach devised by Lie is one of the most successful techniques
available for solving these equations. However, many second order equations cannot be reduced
to quadratures due to the lack of a sufficient number of point symmetries. We observe that
increasing the order will result in a third order differential equation which, when reduced via an
alternate symmetry, may result in a solvable second order equation. Thus the original second
order equation can be solved.
In this dissertation we will attempt to classify second order differential equations that can
be solved in this manner. We also provide the nonlocal transformations between the original
second order equations and the new solvable second order equations.
Our starting point is third order differential equations. Here we concentrate on those invariant
under two- and three-dimensional Lie algebras
