Systems of Clairaut type
Systems of Clairaut type
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Clairaut 型系统
DOI：
10.4064/cm-66-2-219-226
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发表时间：
1992
期刊：
影响因子：
--
通讯作者：
S. Izumiya
中科院分区：
文献类型：
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作者：
S. Izumiya
大约260年前，Alex Claude Clairaut [1]研究了下面的方程，现在称为Clairaut方程：y = x ^ -f /（^）。它通常在大学微积分的一、二年级课程中讲授，并被视为非线性方程组的典型例子之一，很容易求解。此外，它有一个非常漂亮的几何结构如下：存在一个由直线y = t x Hf（i）组成的“通解”，其中t是一个参数，奇异解是这样一个族的包络（图1）。
About 260 years ago Alex Claude Clairaut [1] studied the following equation which is called the Clairaut equation now : y = x ^ -f /(^). It is usually taught in the first or second year course of calculus in the university and treated as one of the typical examples of non-linear equations that are easily solved. Moreover it has a quite beautiful geometric structure as follows : There exists a "general solution" that consists of lines y = t x Hf ( i ) , where t is a parameter and the singular solution is the envelope of such a family (Fig. 1).