Invertible point transformations, Painlevé test, and the second Painlevé transcendent
The rather complicated condition given by Euler et al. (1989) that the anharmonic oscillator \(u''+f_ 1(t)u'+f_ 2(t)+f_ 3u^ 3=0\) passes the Painlevé test is shown to be identical to the condition that the anharmonic oscillator can be transformed to the second Painlevé transcendent.
nonlinear ordinary differential equations
scientific article; zbMATH DE number 4208522
scientific article