The General Solution of One Kind of 3-order Variable Coefficients Linear Ordinary Differential Equation

In this paper,one kind of 3-order variable coefficients Linear ordinary differential equation y+A(x)y″+B(x)y′+D(x)y = E(x)is discussed when the conditions D~2+DB′-BD′=0 and BD+DA′-AD′=0 are met.Its general solution can be found through the elementary integral method,from which the general solution formulas are derived.