Anisotropic relativistic fluid spheres in the Buchdahl model

In this work, we present a class of relativistic and well-behaved solution to Einsteins field equations describing anisotropic matter distribution. We perform our analysis by proposing a Buchdahl ansatz which represents almost all the known analytic solutions to the spherically symmetric, static Einstein equations with a perfect fluid source, including, in particular, the Vaidya-Tikekar. We have considered three different cases for generalized Buchdahl dimensionless parameter K. Our suggested solution is free from physical and geometric singularities, satisfies causality condition, and relativistic adiabatic index(gamma), and exhibits well-behaved nature, as well as, all energy conditions and equilibrium condition are well-defined, which implies that our model is physically acceptable.