一类二阶变系数线性微分方程的初值问题

the Initial Problems of Second Order Linear Differential Equation with Variable Coefficient

《常微分方程》[1-3]中,通常利用特征方程法和常数变易法来求解常系数线性微分方程问题。而变系数的常微分方程,尽管理论上证明了解的存在唯一性,但具体求解尚无通法。通过利用Laplace变换来讨论二阶变系数线性微分方程在变系数是自变量的一次式的情形下的初值问题。

The characteristic equation method and method of variation of constant is applied in solving linear differential equation with constant coefficients in ordinary differential equation. Otherwise, existence and uniqueness of solution of linear differential equation with variable coefficient was proved in theory that is no general method to solve it. This paper solves the initial problems of second order linear differential equation with variable coefficient by Laplace transform.