Articles you may be interested inThe Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann systemWe use the known relationship between the Lagrangian and Jacobi's ͓Vorlesungen über Dynamik. Nebst fünf hinterlassenen Abhandlungen desselben herausgegeben von A Clebsch ͑Druck und Verlag von Georg Reimer, Berlin, 1886͔͒ last multiplier of second-order ordinary differential equations to determine two first integrals and their Noether ͓Nachr. Ges. Wiss. Goettingen Math. Phys. Kl. 2, 235 ͑1918͔͒ symmetries for the Fuch's solution ͓C. R. Acad. Sci. 141, 555 ͑1905͔͒ of Painlevé VI after finding two Lagrangians in addition to known Hamiltonian given by Malmquist ͓Ark. Mat. Astr. Fys. 17, 1 ͑1922͔͒. The general solution follows and we show it to be the same as given by Fuchs.