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On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y''=A(x,y)y'+B(x,y)$
P. V. Bibikov V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
Abstract:
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 $y''=A(x,y)y'+B(x,y)$, in which the coefficients $A$ and $B$ are rational in $x$ and $y$.
Keywords:
ordinary differential equation, symmetry group, jet space, differential invariant.
Received: 17.09.2017
Citation:
P. V. Bibikov, “On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y''=A(x,y)y'+B(x,y)$”, Mat. Zametki, 104:2 (2018), 163–173; Math. Notes, 104:2 (2018), 167–175
Linking options:
https://www.mathnet.ru/eng/mzm11802https://doi.org/10.4213/mzm11802 https://www.mathnet.ru/eng/mzm/v104/i2/p163
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Abstract page: | 341 | Full-text PDF : | 57 | References: | 42 | First page: | 31 |
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