The problem studied here focuses on a compact manifold M without boundary in which the Riemannian metric g is on Λ = M – {p1, p2,…,pκ}. Near the pi 's, g has a particular type of singularity in which locally M = (0, δ)x × Ywhere Y is a Riemannian manifold with metric h. Calculation techniques involving Christoffel symbols, scalar curvature, and the Lapalacian of the manifold are used to reduce the Yamabe equation to a system of partial differential equations. After assuming that a function u > 0 satisfying the Yamabe equation exists, the most singular partial differential equation is solved using integration techniques to find necessary conditions on Y and h. Also studied in this paper are the conditions on Y and h for which M is already a manifold with constant scalar curvature.