The generalized Painlevé–Ince equation is integrable only when β = α²/9, a known result, while the paper's claim about passing the Painlevé test under inversion is not properly derived.
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A Systematic Analysis of the Properties of the Generalised Painlev\'e--Ince Equation
The generalized Painlevé–Ince equation is integrable only when β = α²/9, a known result, while the paper's claim about passing the Painlevé test under inversion is not properly derived.