2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80830A method of calculating a new class of symmetries is presented for partial differential equations. The method give a new dynamical solution for an isothermal and cylindrically symmetric hydrodynamics equations under self-gravity. The solution describes a development of a gas cylinder from a motion-less state to states of expansion and oscillation.Exactly Solvable and Integrable Systemstext