In this paper it is focused on the conversion of partial differential equations to certain universal forms whose series solutions can be constructed via two term recursions. In order to obtain a universal form the space extension concept is used. The equation is converted into a new form by increasing the number of unknowns in such a way that the resulting equation is obtained in a vector valued form. This procedure is called as space extension approach. The new universal form which is the main goal of this work permits us to get its solution via series whose coefficients satisfy two term recursions. However, we do not give this procedure here in details since we consider the application of space extension concept as the most important aspect of the work. Instead, certain clues about the solution technique construction are also presented.