负 m 次幂函数与排列数的交错级数型线性微分方程

摘要

使用数学归纳法证明了把系数中含有负 m 次幂函数与排列数的交错级数型线性微分方程化为可逐次积分的线性微分方程结论，并给出了求解此类方程通解的方法，最后通过例子进行了说明。%Mathematical induction is used to prove the conclusion that the alternating series type of linear differential equation of negative m numbers of times of power function and number of permutation is reduced to successive integral linear differential equation, and the general solution to this kind of equations is provided with examples following.