Geodesic
On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y''=A(x,y)y'+B(x,y)$
Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 163-173

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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, differential invariant.
Mots-clés : jet space 
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     author = {P. V. Bibikov},
     title = {On {Differential} {Invariants} and {Classification} of {Ordinary} {Differential} {Equations} of the {Form} $y''=A(x,y)y'+B(x,y)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {163--173},
     publisher = {mathdoc},
     volume = {104},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a0/}
}
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P. V. Bibikov. On Differential Invariants and Classification of Ordinary Differential Equations of the Form $y''=A(x,y)y'+B(x,y)$. Matematičeskie zametki, Tome 104 (2018) no. 2, pp. 163-173. http://geodesic.mathdoc.fr/item/MZM_2018_104_2_a0/