Computation of complex -coefficient complex -solution differential equations is a problem that arises in various domains of science and engineering. This paper aims at applying the Theory of Characteristic Modes (TCM) approach along with the Method of Moments (MoM) in solving these problems with emphasis on procedures for higher differential equations. Several available methods, known in literatures, are available for solving the problem. The complexity of the available methods differs based on the accuracy of the solution. In this paper, the general method is first presented and then a simplified version of it is proposed to solve high order differential equations. Two examples are illustrated, a third and a fourth order complex-coefficients complex-solution differential equations, to show the simplicity of the proposed method. The proposed approach can be also introduced along with other methods to solve these special occurrences differential equations and other boundary value problems.