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In this paper, by using the theories and methods of mathematical analysis and computer algebra, a new algorithm of symbolic integral was established, a new Maple procedure myint for it was established, too. And it was applied to the automatic proving the mean-value theorems for derivatives. The results indicated that the algorithm of symbolic integral had been established in this paper had advantage of simple idea, excellent property for operation and powerful competence. This would be useful for the problem of solving differential equations, automatic proving some mathematical theorems, and so on. [Copyright &y& Elsevier]

Abstract: In this paper, by using the theories and methods of mathematics analysis, ordinary differential equation and computer algebra, a reliable algorithm for solving ordinary differential equation (ODE) was established, and a new Maple procedure mechodeproc was established, too. The results of the examples indicated that the procedure mechodeproc based on Taylor polynomial method was simple and effective, and could provide an accuracy approximate solution or exact solution of the ordinary differential equation. This would be useful for solving differential equation. [Copyright &y& Elsevier]