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A new analytical method for finding the general solution of the nth-order linear differential equation with variable coefficients is given based on generalizing the idea of differential transfer matrix method already proposed for solving the second order Helmholtz equation. Our generalization has two aspects. First, the given formulation copes with the nth-order linear differential equations, rather than the special case of second order wave equations. Second, the proposed approach is generalized in several different ways each yielding different types of differential transfer matrices with correspondingly different numerical accuracies. The presented methods can be applied to problems such as analysis of linear time varying systems like linear circuits with time varying elements, in homogeneous transmission lines, etc.