The computer generated symbolic solution of a system of linear first order differential equations

AbstractThe computer generated symbolic Cayley-Hamilton recursion solution of the matrix equation dx/dt = Ax is obtained using the PL/I-FORMAC Interpreter. The generated solution is a polynomial whose degree is larger than the order of A. The Leverrier method is then used to generate the characteristic polynomial of A and the Cayley-Hamilton theorem is used to reduce powers of A in the solution. This method has applications in the area of networks of RCL circuits and networks of mechanical circuits. In the area of statistics, the explicit solution of multi-component generalized birth-death stochastic processes can be obtained. Finally, our linear system also represent many input-output economic models, as well as input-output models in other social sciences and business analysis