On Differential Invariants and Classification of Ordinary Differential Equations of the Form y'' = A(x, y)y' + B(x, y)
- 作者: Bibikov P.V.1
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隶属关系:
- Trapeznikov Institute of Control Sciences
- 期: 卷 104, 编号 1-2 (2018)
- 页面: 167-175
- 栏目: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/151164
- DOI: https://doi.org/10.1134/S0001434618070180
- ID: 151164
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详细
The class of second-order ordinary differential equations y'' = A(x, y)y' + B(x, y) is studied by methods of the geometry of jet spaces and the geometric theory of differential equations. The symmetry group of this class of equations is calculated, and the field of differential invariants of its action on equations is described. These results are used to state and prove a criterion for the local equivalence of two nondegenerate ordinary differential equations of the form y'' = A(x, y)y' + B(x, y), inwhich the coefficients A and B are rational in x and y.
作者简介
P. Bibikov
Trapeznikov Institute of Control Sciences
编辑信件的主要联系方式.
Email: tsdtp4u@proc.ru
俄罗斯联邦, Moscow, 117997
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