A Finite Recursive Method for Particular Solution of a Class of Linear ODE with Constant Coefficients

To find a particular solution of a linear ordinary differential equation with constant coefficients,in which,the nonhomogeneous part f(x) is a polynormial;an exponential function;a sine or cosine function or a production of them,a finite recursive method is presented in this paper.It is better than the current undetermined coefficient method since it is a uniform method for different cases of f(x);can solve high order problems;is easy for computing and can get the analytic particular solution in finite steps.