  It is known that Ermakov-Pinney equation is a nonlinear equation with wide
applications in dynamics, physics, cosmology (e.g., Ermakov equation can be
connected to Bose-Einstein Condensate cosmology which unifies the dark energy
and the dark matter). In this analytical study, we have presented a new type of
solving procedure to obtain analytical solution of Ermakov-Pinney equation,
specifically for the case of rotating early Universe with vortex. The
particular case of solution of the aforementioned equation is presented also
(such the solution of special kind is important for cosmological applications)
which corresponds to the class of solutions with symmetry reduction.
