Volume 18, Issue Supplement 1, September 2011, Pages 237 - 250
Second-Order Ordinary Differential Equations with First Integrals of the Form C(t) + 1/(A(t, x)ẋ + B(t, x))
Received 30 September 2010, Accepted 10 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001398How to use a DOI?
- Keywords
- Ordinary differential equations; symmetries; first integrals; linearization
- Abstract
We study the class of the ordinary differential equations of the form ẍ + a2(t, x)ẋ2 + a1(t, x)ẋ + a0(t, x) = 0, that admit v = ∂x as λ-symmetry for some λ = α(t, x)ẋ + β(t, x). This class coincides with the class of the second-order equations that have first integrals of the form C(t) + 1/(A(t, x)ẋ + B(t, x)). We provide a method to calculate the functions A, B and C that define the first integral. Some relationships with the class of equations linearizable by local and a specific type of nonlocal transformations are also presented.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - C. Muriel AU - J. L. Romero PY - 2021 DA - 2021/01/07 TI - Second-Order Ordinary Differential Equations with First Integrals of the Form C(t) + 1/(A(t, x)ẋ + B(t, x)) JO - Journal of Nonlinear Mathematical Physics SP - 237 EP - 250 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001398 DO - 10.1142/S1402925111001398 ID - Muriel2021 ER -