ABSTRACT
In the case of a simultaneous system of M equations with M dependent variables, there are linear operators with constant coefficients, and its determinant specifies the characteristic polynomial of the system of simultaneous differential equations, whose order N is the degree of the characteristic polynomial. The solutions corresponding to single or multiple, real or complex roots, are similar for a single (set of simultaneous) differential equation(s), and each dependent variable is a linear combination of them, with coefficients determined by the initial conditions. The case of a single (set of simultaneous) linear ordinary differential equation(s) with constant coefficients and a forcing term, can be considered using the characteristic polynomial directly or as an inverse operator. A characteristic polynomial also exists for a single (set of simultaneous) linear ordinary differential equation(s) with power coefficients, leading to similar methods of solution.
