二阶变系数线性微分方程的求解定理

先提出引理,即某函数是二阶变系数线性齐次微分方程的解的充要条件,再给出在已知二阶变系数线性齐次微分方程的某一解的条件下,二阶变系数线性非齐次微分方程的通解公式——即定理1,然后借助引理及定理1提供了几类二阶变系数线性非齐次微分方程通解的积分表达式,从而获得求几类方程通解的统一方法.

The Theorem for Solving the Second Order Linear Differential Equation with Varied Coefficients

First,a lemma is introduced,which gives the necessary and sufficient condi tion for having solutions of homogeneous second order linear differential equation with varied coefficients. Second,a general formula is given, which solves non-homogeneous second order linear differential equation with varied coefficients on a condition of having solutions for ho mogeneous secoud order linear differential equation with varied coefficient-theorem 1 Then, by the lemma and theorem 1 several formulae of integration are obtained, which solves like non-homogeneous second order differential equation with varied coefficient. At last,a unitary method for solving general solutions of such like is obtained.