Abstract
We present a nonlocal symmetry method to reduce scalar first- and second-orderordinary differential equations (ODEs) to quadratures. It is shown that a second-orderODE admitting a non-Abelian two-dimensional Lie algebra of point symmetriesis reducible to quadratures via a nonideal of the algebra. We also providea direct method of integration for a first-order ODE admitting an exponential nonlocal symmetry which satisfies an additional property.Moreover, we give examples, two on double reduction and several on Abel equations of the second kind, that illustrate ourapproaches.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.