求常系数线性微分方程通解的降阶方法探索

Exploration of the Derogatory Method of General Solution to Linear Differential Equation of Constant Coefficient

对于 n 阶常系数线性微分方程,若 r_0是所对应的特征方程的 K 重根(1≤k≤n),作变换y=e^ro^zz 代入原方程,使其化为 n-k 阶微分方程,起了降阶作用.本文给出了求常系数线性方程通解的降阶方法.

For a n-order linear differential equation with constant coefficients,if Υ_0 is the K- fold root of the corresponding characteristic equation(1≤K≤n),altering y=e^r0~z and substituting it into the original equation,which is then changed to a(n—K)order differen- tial equation,i.e.a derogation happens.The derogatory method of solving the general inte- grals for the linear differential equation with constant coefficients has been given.