Lagrangians for equations of Painlevé type by means of the Jacobi last multiplier. (English) Zbl 1362.49021
Summary: We apply the method of Jacobi last multiplier to the fifty second-order ordinary differential equations of Painlevé type as given in Ince in order to obtain a Lagrangian and consequently solve the inverse problem of Calculus of Variations for those equations. The easiness and straightforwardness of Jacobi’s method is underlined.
Keywords:
ordinary differential equations; equations of Painlevé type; Lagrangians; Jacobi last multiplierReferences:
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