Abstract：In view of the problem of integrable property of ordinary differential equations, a new method is adopted, which is different from the method that reduced order and elimination. In this paper, the method of using three order ordinary differential equation action on Lie group used the theory of symmetric group. By means of a transformation, the solution of the equation is transformed into another solution of the equation in order to find out Lie group generating element and get the first integral. On this basis, this paper analyzes the problem of integrable property of differential equation. The results of the study show that the three order differential equations are not integrable under the action of the symmetric group, and at the same time, the research object is extended from the second order differential equation to the three order differential equation.
孙丹阳,盖如栋. 常规三阶常微分方程在对称群作用下的可积性[J]. 辽宁工程技术大学学报(自然科学版), 2017, 36(2): 206-209.
SUN Danyang,GAI Rudong.. Integrable properties of three order ordinary differential equations under the action of the symmetry group. Journal of LNTU.Natural Science, 2017, 36(2): 206-209.