Abstract
Although symmetry analysis provides a powerful tool for solving differential equations, it has not proved to be as successful in the treatment of initial-value and boundary-value problems. A possible reason for this is the belief that the set of symmetries of an initial-value problem is a subset of the symmetries of the associated governing differential equation. It was recently shown that this is, in fact, not the case and a method introduced for constructing the symmetries of a class of initial-value problems using Taylor series. The present thesis extends this method to arbitrary-order regular ordinary differential equations subject to both an arbitrary-order single initial condition and an arbitrary linear combination of single initial conditions. Furthermore, a practical method for dealing with a class of initial-value problems that possess a regular singularity is developed, through the use of the Frobenius method.