In many instances, it is not possible to obtain the solution of an ordinary differential equation of the type of eq. (1.2) in a closed form. If the differential equation (1.2) has ao(x) as a non-vanishing bounded functions and al(x), ~(x), ... , ~(x) are bounded in the interval a::; x ::; b, satisfying the system in eq. ( 1.29), then there exists a set of n solutions Yi(x), i = 1, 2, ... , n. Such a solution can be expanded into a Taylor series about a point Xo• a < x0 < b, such that:



are not determinable from eq. (2.2). However, one can assume that the solution to eq. (1.2) has a power series of the form in eq. (2.1) and then the unknown constants en can be determined by substituting the solution ofeq. (2.1) into eq. (1.2).