Through the introduction to the properties of characteristic polynomial, the order reduction theorem of the characteristic polynomial as well as its application in high order matrix is studied, and also a simplified method (characteristic polynomial method), which is used to solve the particular integral of the non-homogeneous linear differential equation with constant coefficients, is proposed in this paper. It is simpler than coefficient comparison and Laplace transform method, and also is of greater realistic significance for the differential equations with high order number and terms number.
On an order reduction theorem in the Lagrangian formalism
