二阶变系数线性微分方程与其对应的Riccati方程可积的等价性及应用

Equivalence and Applications of Second Order Linear Differential Equations with Variable Coefficients and Integrability of Their Corresponding Riccati Equations

揭示了二阶变系数线性非齐次微分方程与其对应的Riccati方程可积是等价的,二阶变系数线性齐次微分方程与其对应的Riccati方程可积是等价的,并给出了二阶变系数线性微分方程在其对应的Riccati方程有特解下的求解公式.

The equivalence on Homogeneous and Non-homogeneous second order linear differential equations with variable coefficients and integrability of their corresponding Riccati equations was established.Furthermore,the formula of solution to second order linear differential equations with variable coefficients is given if their corresponding Riccati equation has special solutions