Geodesic
On Lie’s problem and differential invariants of ODEs $y''=F(x,y)$
Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 16-25

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A point classification of ordinary differential equations of the form $y''=F(x,y)$ is considered. The algebra of differential invariants of the action of the point symmetry pseudogroup on the right-hand sides of equations of the form $y''=F(x,y)$ is calculated, and Lie's problem on the point equivalence of such equations is solved.
Mots-clés : point transformation, pseudogroup, jet space
Keywords: differential invariant, Lie's problem. 
@article{FAA_2017_51_4_a1,
     author = {P. V. Bibikov},
     title = {On {Lie{\textquoteright}s} problem and differential invariants of {ODEs} $y''=F(x,y)$},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {16--25},
     publisher = {mathdoc},
     volume = {51},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a1/}
}
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P. V. Bibikov. On Lie’s problem and differential invariants of ODEs $y''=F(x,y)$. Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 4, pp. 16-25. http://geodesic.mathdoc.fr/item/FAA_2017_51_4_a1/