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We describe a method to generate nonlocal constants of motion for a special class of nonlinear ODEs. We employ the method of the generalized Sundman transformation to obtain certain new nonlocal first integrals of autonomous second-order ordinary differential equations belonging to the classification scheme developed by Painlevé and Gambier.

Nonlocal Constants of Motions of Equations of Painlevé – Gambier Type and Generalized Sundman Transformation