常数变易法在线性非齐次常微分方程求解中的重要注解

Notes of Variation of Constants for Solving Linear Nonhomogeneous ODE

本文关注常数变易法在n阶线性非齐次常微分方程求解中的特性,且特别针对二阶微分方程.定理1给出了非齐次方程通解与该任意常数无关的充分条件,通过两个典型算例验证了定理1中的结论,分析了不同约束条件对通解的影响.

The method of variation of constants for solving n^(th) order,especially for the 2^(nd) order,linear nonhomogeneous ODE is discussed.Theorem 1 presents a sufficient condition for determining the general solution independent of the arbitrary constants.With two classical numerical examples,we verify the result of Theorem 1 and explore further the effects of different constrains to the general solution.