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§1.引言十九世紀二十年代,Cauchy在严格奠定数学分析的基础上,认定前人毫无根据地相信通解的存在,并以此为出发点先求通解,然后确定常数以决定特解的办法是不科学的。他把求特解和証明特解的存在提到首要地位,于是提出了带有初始条件的所謂哥西問題。約在1830年左右,他給出了方程dy/dx=f(x,y)带有初始条件x=x_0时y=y_0的解的存在和唯一性的第一个証明。首先是在右端函数为解析的条件下采用优函数的方法証明的。其次,他在f和(?)的連續假設下証明了解的存在唯一性(証明概要发表于1835年)。
§ 1. INTRODUCTION In the 1920s, Cauchy, on the basis of strict mathematical analysis, determined that his predecessors had unfounded beliefs in the existence of general solutions. They used this as a starting point to seek general solutions, and then determined constants to determine specific solutions. It is unscientific. He mentioned the existence of special solutions and the existence of specific solutions, and he proposed the so-called Geshe problem with initial conditions. Around 1830 he gave the first proof of the existence and uniqueness of the solution dy/dx=f(x,y) with the initial condition x=x_0 and y=y_0. The first is proved by the method of using the superior function under the condition that the right-end function is parsed. Second, he proved the existence and uniqueness of the understanding under the assumptions of f and (?) (the proof summary was published in 1835).