Solving homogeneous linear differential equations of order 4 in terms of equations of smaller order.

Abstract

In this thesis we consider the problem of deciding if a fourth order linear differential equation can be solved in terms of solutions of lower order equations. There is a group theoretic criteria which can be turned into a decision procedure for solving this problem. Once the decision has been made that a certain type of equation can be solved in terms of lower order equations we also give methods for producing the lower order equations used for solving it.