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It is known that Ermakov-Pinney equation is a nonlinear equation with wideapplications in dynamics, physics, cosmology (e.g., Ermakov equation can beconnected to Bose-Einstein Condensate cosmology which unifies the dark energyand the dark matter). In this analytical study, we have presented a new type ofsolving procedure to obtain analytical solution of Ermakov-Pinney equation,specifically for the case of rotating early Universe with vortex. Theparticular 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.

Revisiting solving procedure for Ermakov-Pinney equation (with applications in the field of cosmology)