In this paper,using the method of variation of constant,some new conditions of integrability on the Abel equation and Riccati equation are given.

The existence of particular solutions for a class of Riccati equations is studied by means of variation of constants and initial integral methods.

In this paper,using total differentiation method and variation of constants,we give general solution formula of Bernoulli equation with different methods.

Demonstrated in this paper is how the Constant-transform method,the typical method for solving differential equations of order one,is used in solving linear differential equations of order four.

Demonstrated in this paper is how the Constant-transform method, the typical method for solving differential equations of order one, is used in solving linear differential equations of order three.

This article derives the general solution of linear differential equation with constant coefficient changing .

In addition to the routine in which we can use variable shift to change Bernoulli equations into linear equations for solutions,we can also directly use constant variation for solutions,then find out some solutions of the one-step nonlinear differential equations.

This paper begins with the equation of the structural characteristics,gives the mathematical principles of the constant variation of its general solution and simplifies the method of integrating factor.