RT journal article
T1 λ-Symmetries and integrability by quadratures
A1 Muriel Patino, María Concepción
A1 Romero Romero, Juan Luis
A1 Ruiz Serván, Adrián
A2 Matemáticas
K1 λ−symmetries
K1 first integrals
K1 integrating factors
K1 Jacobi last multiplier
AB 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 Painleve- 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.
PB Oxford University Press
SN 1464-3634
YR 2017
FD 2017
LK http://hdl.handle.net/10498/33829
UL http://hdl.handle.net/10498/33829
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026