Exact anisotropic sphere with polytropic equation of state

We study static spherically symmetric spacetime to describe compact objects with anisotropic matter distribution. We express the system of Einstein field equations as a new system of differential equations using a coordinate transformation, and then write the system in another form with polytropic equation of state and obtain two classes of exact models. The models satisfy all major physical features expected in a realistic star. For polytropic index n?=?2, we obtain expressions for mass and density which are comparable with the reported experimental observations.