二阶变系数线性微分方程的通解

The General Solution of Second Order Linear Differential Equations with Variable Coefficient

利用特解讨论了二阶变系数齐次线性微分方程,得到了形如y=y*{c1∫(y*)-2 exp[-∫p(x)d x]dx+c 2}的通解公式,同时,利用常数变易法得到了非齐次方程的通解,改进和推广了相关文献中的结论。

A second order linear differential equation with variable coefficient has been studied, and a general solution is given by use of the special solution, as follows y=y^＊{c1∫（y^＊）^-2exp[-∫p（x）dx]dx＋c2}. Meanwhile, the general solution of inhomogeneous equation is given by use of the method of variation of constant. Some recent results in relative articles are extended and improved.