Equivalence Classes, Symmetries and Solutions of Linear Third Order Differential Equations

The subject of this article are third-order differential equations that may be linearized by a variable change. To this end, at first the equivalence classes of linear equations are completely described. Thereafter it is shown how they combine into symmetry classes that are determined by the various symmetry types. An algorithm is presented allowing it to transform linearizable equations by hyperexponential transformations into linear form from which solutions may be obtained more easily. Several examples are worked out in detail.