求一类常系数线性常微分方程特解的有限递推法

对于非齐次项为多项式,指数函数,正(余)弦函数,或它们的乘积形式的常系数线性常微分方程,提出了求其特解的有限递推法.它方法统一,计算简洁,便于编程,能解决高阶问题,能在有限步内得出方程的解析特解,因而优于目前广泛采用的待定系数法.

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.