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This paper applies a nonlinear differential equation to the information management system of college course selection. A teaching information management system based on an approximate learning strategy is presented by using statistical linearization technology. An imprecise controller is obtained by numerical simulation of Riccati differential equations with statistical linearization. This kind of Riccati differential equation differs significantly from the ordinary one. Then the system proposes a collaborative filtering method based on nonlinear differentiation based on student feature classification. At last, this paper systematically analyzes the differences between course selection systems, business recommendations, and student attributes—the system experiments on college students' choice of a learning platform. The study found that the method was correct 34.6% of the time. This system can provide practical guidance for students to choose courses.