Abstract
We present a certain class of second order nonlinear differential equations containing the first Painlevé equation (PI). Each equation in it admits the quasi-Painlevé property, namely every movable singularity of a general solution is at most an algebraic branch point. For these equations we show some basic properties.
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Shimomura, S. A class of differential equations of PI-type with the quasi-Painlevé property. Annali di Matematica 186, 267–280 (2007). https://doi.org/10.1007/s10231-006-0004-3
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DOI: https://doi.org/10.1007/s10231-006-0004-3