The equations of Spinodal Decomposition as postulated by Cahn and Hilliard involve a fourth-order partial differential equation, which to date has not been solved analytically. In this article, these equations are examined in their various versions, and solutions are obtained for the steady state and transient forms using multiple methods. Then the moving boundary associated with transformation is reviewed using a heat transfer approach, and a solution is attempted using a series and a similarity transformation approach. The equation is postulated to have two contributions, one from the usual Laplacian and Fickian contribution part for which Stefan solutions are known, and one with a Double Laplacian, which has not been examined. The thin film approximation is applied to simplify some parts of the analysis and to try to get a numerical solution. Applicability in the analysis of MGA's is discussed.