We suggest an algorithm for integrating systems of two second-order ordinary differential equations with four symmetries. In particular, if the admitted transformation group has two second-order differential invariants, the corresponding system can be integrated by quadratures using invariant representation and the operator of invariant differentiation. Otherwise, the systems reduce to partially uncoupled forms and can also be integrated by quadratures.
- Received June 9, 2016.
- Accepted December 5, 2016.
- © 2017 The Author(s)
Published by the Royal Society. All rights reserved.