Linearization of second-order ordinary differential equations by generalized Sundman transformations (Q543945)

The authors analyze the application of the generalized Sundman transformation for the linearization problem. The obtained results show that previous investigations [\textit{L. G. S. Duarte, I. C. Moreira} and \textit{F. C. Santos}, J. Phys. A, Math. Gen. 27, No.~19, L739--L743 (1994; Zbl 0845.34011)] are not complete. The given examples show that, in contrast to point transformations (S. Lie results), for a linearization problem via the generalized Sundman transformation one has to use the general form of a linear second-order ordinary differential equation instead of the Laguerre form.