Computation of local symmetries of second-order ordinary differential equations by the Cartan equivalence method

The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular, we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries) into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form of the Lie system is found explicitly.