By using transformation thought,this paper obtains the focus chord of all kinds of conic section through analyzing a sample in conic section teaching.

The variable thoutht of Chinese ancient mathematics is expounded in terms of coordinate thought,the thought of the equation and function,the limit idea and calculus thought which had underlain the Chinese ancient mathematics.

With variable substitution,several kinds of linear differential equations are solved and several sufficient and necessary conditions are obtained.

The method searching for solutions to first order non liner equation with variable substitution and integral gene, and the method searching for solutions to all the integral with integral gene were discussed and expounded in this paper.

This paper uses variable substitution to discuss the methods of solving three integral kinds of function-coefficient differential equations of the third order.

With proper method of variable substitution, the soluble method to two kinds of inegrable equation of Riccati form is found, and the general integral expressions are given.