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- Title
λ-Symmetries and integrability by quadratures.
- Authors
MURIEL, C.; ROMERO, J. L.; RUIZ, A.
- Abstract
It is investigated how two (standard or generalized) λ-symmetries of a given second-order ordinary differential equation can be used to solve the equation by quadratures. The method is based on the construction of two commuting generalized symmetries for this equation by using both λ-symmetries. The functions used in that construction are related with integrating factors of the reduced and auxiliary equations associated to the λ-symmetries. These functions can also be used to derive a Jacobi last multiplier and two integrating factors for the given equation. Some examples illustrate the method; one of them is included in the XXVII case of the Painlevé- Gambier classification. An explicit expression of its general solution in terms of two fundamental sets of solutions for two related second-order linear equations is also obtained.
- Subjects
SYMMETRIES (Quantum mechanics); DIFFERENTIAL equations; MULTIPLIERS (Mathematical analysis); JACOBI polynomials; JACOBI operators
- Publication
IMA Journal of Applied Mathematics, 2017, Vol 82, Issue 5, p1061
- ISSN
0272-4960
- Publication type
Article
- DOI
10.1093/imamat/hxx024