大学生数学竞赛常微分方程试题的一题多解

Multiple Solution Methods to a Differential Equation Problem of the College Mathematics Competition

摘要: 本文对第十七届非数学类大学生数学竞赛中的一道常微分方程试题，从不同角度出发，给出了六种解题方法，旨在拓展发散思维，跳出固定套路，并且对比优劣，学会择优解题。本文还找到了该方程的常数解，更全面地考虑问题。

Abstract: This paper presents six distinct solution methods for an ordinary differential equation problem from the 17th National College Mathematics Competition (Non-Mathematics Category). It aims to help students broaden their divergent thinking, break away from fixed routines, and learn to select the optimal approach by comparing the advantages and disadvantages of each method. Furthermore, this study identifies the constant solution of the equation, encouraging students to consider problems from a more comprehensive perspective.