－类非线性微分方程解空间显易结构的唯一性

ON UNIQUENESS ABOUT THE EXPLICIT STRUCTURE OF SOLUTION SPACE OF ONE TYPE OF LINEAR DIFFENTIAL EQOATION

对所有形如的方程的集合Ｅ（Ｄ），引入线性变换群Ｇ（Ｄ），从而将Ｅ（Ｄ）进行等价分类，并由此提出解空间显易结构唯一性概念，指出Ｂｅｒｎｏｕｌｌｉ类方程具第一显易结构，但其显易结构不唯一，而任何非Ｂｅｒｎｏｕｌｌｉ类方程着具显易结构，则其显易结构必唯一．

The conceptions of the linear transformation group, the equivalent relation and the equivalent class are introduced to the differential equationin the complex domain, and a definition of uniqueness of the explicit structure of solutionspace is proposed. Based on this definition. the Bernoulli type equation and thenon-Bernoulli type equation are studied.