title: Integrability of systems of two second-order ordinary differential equations admitting four-dimensional Lie algebras.
abstract: 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.
authors.affiliation: Laboratory 'Group analysis of mathematical models in natural and engineering sciences' , Ufa State Aviation Technical University , 450 008 Ufa, Russia.
authors.forename: A A
authors.identifier: 0000-0002-4424-6104
authors.initials: AA
authors.lastname: Gainetdinova
authors.affiliation: Laboratory 'Group analysis of mathematical models in natural and engineering sciences' , Ufa State Aviation Technical University , 450 008 Ufa, Russia.
authors.forename: R K
authors.initials: RK
authors.lastname: Gazizov
keywords: differential invariants; four-dimensional Lie algebras of operators; operator of invariant differentiation; systems of two second-order ordinary differential equations