二阶变系数线性微分方程通解的进一步研究

A Further Research on General Solution to Second-order Linear Differential Equation with Variable Coefficients

针对求二阶变系数线性微分方程的解未给出详细的研究,而在实际中有时要用到一般的求解法的情况,经过变量替换和算子理论以及恰当方程的处理方法来达到降阶,通过降阶法转化为求一阶线性微分方程的通解,从而达到对二阶变系数线性微分方程通解的进一步研究的目的.

This paper is to find a general solution to second- order linear differential equation with variable coefficients, which is not deeply researched and yet is applied in practice sometimes. The method is order induction, which is achieved by variable substitution,linear operator theory and treatment of appropriate equation, that is to say, the second- order equation is induced into first one.