Abstract
A Maple procedure for the analytical solving of second-order ordinary differential equations admitting two known λ-symmetries is presented. The approach is based on the construction of two commuting generalized symmetries for the equation by using both λ-symmetries. From these two commuting symmetries, two functionally independent first integrals of the equation arise by quadratures. The set of routines includes a solver for these types of equations, and commands for the explicit determination of: integrating factors of the reduced and auxiliary equations associated with the λ-symmetries; a Jacobi last multiplier; and two integrating factors for the given equation.
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Acknowledgements
J. Mendoza thanks the support of Programa Iberoamericano de Formación de Doctores en Ciencias Básicas during his stay at the University of Cádiz (Spain) in 2019.
C. Muriel acknowledges the financial support from FEDER—Ministerio de Ciencia, Innovación y Universidades—Agencia Estatal de Investigación by means of the project PGC2018-101514-B-I00 and Junta de Andalucía to the research group FQM–377.
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Appendix: The Maple Procedure TwoLambdaSym
Appendix: The Maple Procedure TwoLambdaSym
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Mendoza, J., Muriel, C., Vidal, J. (2021). Symbolic Computation Algorithms for Second-Order ODEs by Using Two λ-Symmetries. In: Muriel, C., Pérez-Martinez, C. (eds) Recent Advances in Differential Equations and Control Theory. SEMA SIMAI Springer Series(), vol 9. Springer, Cham. https://doi.org/10.1007/978-3-030-61875-9_5
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DOI: https://doi.org/10.1007/978-3-030-61875-9_5
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