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The linearization problem of a second-order ordinary differential equation bythe generalized Sundman transformation was considered earlier by Duarte,Moreira and Santos using the Laguerre form. The results obtained in the presentpaper demonstrate that their solution of the linearization problem for asecond-order ordinary differential equation via the generalized Sundmantransformation is not complete. We also give examples which show that theLaguerre form is not sufficient for the linearization problem via thegeneralized Sundman transformation.

Linearization of Second-Order Ordinary Differential Equations by Generalized Sundman Transformations