Symmetries and first order ODE patterns

Abstract
A scheme for determining symmetries for certain families of first order ODEs, without solving any differential equations, and based mainly in matching an ODE to patterns of invariant ODE families, is presented. The scheme was implemented in Maple, in the framework of the ODEtools package and its ODE-solver. A statistics of the performance of this approach in solving the first order ODE examples of Kamke's book (E. Kamke, Differentialgleichungen: Lösungsmethoden und Lösungen (Chelsea, New York...

Title of program: Extension to ODEtools package
Catalogue Id: ADIP_v1_0

Nature of problem
Analytical solving of first order ordinary differential equations using symmetry methods.

Versions of this program held in the CPC repository in Mendeley Data
ADIP_v1_0; Extension to ODEtools package; 10.1016/S0010-4655(98)00071-X

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

摘要
针对某类一阶常微分方程（Ordinary Differential Equations, ODEs），本文提出了一种无需预先求解任何微分方程即可确定其对称性的方案，该方案核心通过将ODE与不变常微分方程族的特征模式进行匹配实现。本方案基于ODEtools工具包（ODEtools package）及其ODE求解器的框架，在Maple符号计算软件中完成了实现。本文还统计了该方法在求解Kamke著作《Differentialgleichungen: Lösungsmethoden und Lösungen》（Chelsea出版社，纽约）中的一阶ODE例题时的表现……

程序名称：ODEtools工具包扩展
目录编号：ADIP_v1_0

问题本质
采用对称方法实现一阶常微分方程的解析求解。

Mendeley数据集中的CPC库程序版本
ADIP_v1_0; ODEtools工具包扩展; 10.1016/S0010-4655(98)00071-X

本程序源自贝尔法斯特女王大学维护的CPC程序库（1969-2018）。