二阶变系数线性微分方程的通解

General Solution of a Second Order LDE with Variable Coefficients

通过变量代换,将一类二阶变系数线性微分方程转化为可降阶的微分方程,再利用一阶线性微分方程的解法求解,从而给出了一个运算量较小的通解公式并举例加以应用.

Using variable substitution, a second order linear differential equation with variable coefficients is transformed into a reducible differential equation, and is solved, as the first order linear differential equation, with a formula for general solution which can be calculated easily. Examples are given to verify our method.