Geodesic
Equivalence of second-order ODEs to equations of first Painlev\'e equation type
Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 19-30

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We consider equivalence problem for equations of a degenerate type, which involve, for example, the first Painlevé equation. In terms of algebraic and differential invariants of the family of equations with the cubic nonlinearity in the first-order derivative, we obtain the necessary condition of equivalence to some equations of this type with a known solution. We prove a criterion of equivalence to the first Painlevé equation under point transformations.
Keywords: first Painlevé equation
Mots-clés : equivalence, invariant. 
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     author = {Yu. Yu. Bagderina},
     title = {Equivalence of second-order {ODEs} to equations of first {Painlev\'e} equation type},
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Yu. Yu. Bagderina. Equivalence of second-order ODEs to equations of first Painlev\'e equation type. Ufa mathematical journal, Tome 7 (2015) no. 1, pp. 19-30. http://geodesic.mathdoc.fr/item/UFA_2015_7_1_a2/