Article
Ufa Mathematical Journal
Volume 7, Number 1, pp. 19-30
Equivalence of second-order ODEs to equations of first Painleve equation type
Bagderina Yu.Yu.
DOI:10.13108/2015-7-1-19
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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.