Abstract: It revolves around a pursuit problem related to differential equations.The solution idea is discussed from four aspects,that is,using two different ideas to build a mathematical model.Then find the analytical solution of the model and analyze the effect of the parameters on the solution.Find the numerical solution of the model and analyze the effect of the parameters on the solution.Finally,the simulation implementation of the problem is pursued.Both theoretical and numerical experimental results show when the speed ratio of the smuggling ship and the smuggling ship is greater than 1,the smuggling ship can catch up with the smuggling ship,and the closer the speed ratio is to 1,the longer the required time is.When the speed ratio of the smuggling ship and the smuggler is less than or equal to 1,the smuggling ship can not catch up with the smuggling ship.