常系数非齐次线性微分方程的一个特解公式

A formula to the solutions of initial value problems of linear differential equations with constant coefficients

目的给出非齐次项为拟多项式的常系数非齐次线性微分方程一个特解公式。方法以微分算子为工具,经过巧妙的逻辑推理,通过比较系数给出了特解中多项式的系数计算公式。结果给出了求一类常系数非齐次线性微分方程的特解的递推公式。结论算子方法对常系数线性微分方程的求解可以更进一步得到拓广。

Aim Giving a formula to the linear ordinary differential equations with constant coefficients and quasi-polynomial non-homogeneous terms. Methods By means of using differential opera- tors, ingenious logical deductions and coefficients comparing, the formulae of coefficients of the polynomials in the solutions are determined. Results A recursion formula to the solutions of a class of linear ordinary differential equations with constant coefficients is given. Conclusion The method of differential operators for solving linear ordinary differential equations with constant coefficients can be generalized further.