Complete group classification of systems of two linear second-order ordinary differential equations: the algebraic approach

We give a complete group classification of the general case of linear systems of two second-order ordinary differential equations. The algebraic approach is used to solve the group classification problem for this class of equations. This completes the results in the literature on the group classification of two linear second-order ordinary differential equations including recent results which give a complete group classification treatment of such systems. We show that using the algebraic approach leads to the study of a variety of cases in addition to those already obtained in the literature. We illustrate that this approach can be used as a useful tool in the group classification of this class of equations. A discussion of the subsequent cases and results is given. Copyright (c) 2014 John Wiley & Sons, Ltd.