Generalized symmetries, first integrals, and exact solutions of chains of differential equations
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Muriel, C.
1
- Nucci, M. C. 2
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1
Universidad de Cádiz
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2
University of Messina
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ISSN: 2802-9356
Year of publication: 2021
Volume: 1
Pages: 41-56
Type: Article
More publications in: Open Communications in Nonlinear Mathematical Physics
Abstract
New integrability properties of a family of sequences of ordinary differential equations,which contains the Riccati and Abel chains as the most simple sequences, are studied.The determination ofngeneralized symmetries of thenth-order equation in each chainprovides, without any kind of integration,n−1 functionally independent first integralsof the equation. A remaining first integral arises by a quadrature by using a Jacobi lastmultiplier that is expressed in terms of the preceding equation in the correspondingsequence. The complete set ofnfirst integrals is used to obtain the exact generalsolution of thenth-order equation of each sequence. The results are applied to derivedirectly the exact general solution of any equation in the Riccati and Abel chains