Dissertation (MSc Mathematics)We obtain new exact solutions to the Einstein field equations for anisotropic neutral stellar objects. In our dissertation, we are considering a quadratic equation of state and a choice of measure of anisotropy and metric function adopted from Sunzu’s work. We transform the Einstein field equations for neutral anisotropic matter by adopting the Durgapal and Bannerji’s new variables. We generate the exact solution and hence obtain the gravitational potentials and matter variables from the general differential equation of the model. In our models, we regain the previous anisotropic and isotropic results generated by Sunzu as a special case. It is interesting that our results agree with Minkowski spacetime and earlier Einstein model. The physical analysis of the plots reveals that gravitational potentials and matter variables are well behaved in the interior of the stellar objects. In our model, we generate finite masses which are consistent with astronomical objects found by other researchers.