Explicit Solution for a Family of Hermann Riccati Differential Equations

被引：0
|
作者：
Ritelli, Daniele [1 ]
机构：
[1] Univ Bologna, Dept Stat, Bologna, Italy
来源：
CONTEMPORARY MATHEMATICS | 2022年 / 3卷 / 01期
关键词：
Hermann problem; two steps separation; change of variables; Lambert function;
D O I：
10.37256/cm.3120221302
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with a parametric family of ordinary differential equations originated by an ancient geometric problem posed in 1719 by the Swiss mathematician Jakob Hermann (1678-1733) and partially solved by Jacopo Vincenzo Riccati (1676-1754). We translate Riccati approach. called by himself dimidiata separazione (splitted, or halved, separation), in modern terms and we give the full solution of the Hermann problem completing the partial solution provided by Riccati.
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页码：72 / 80
页数：9
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