Preliminary group classification of \(y''f(x)y^2\) (Q1586180)

The authors use the method of preliminary group classification in order to find forms of \(f(x)\) for which the above differential equation has symmetries. This is made by computing the 4-dimensional Lie algebra of equivalence transformations and then using results of P. Winternitz et al. to find nonsimilar subalgebras. Known cases, given by \textit{P. Kustaanheimo} and \textit{B. Qvist} in [Comment. Phys.-Math., Soc. Fennicae 13, No. 16 (1948; Zbl 0030.28202)], are recovered as well as new symmetry cases determined.