一阶对称形非恰当方程的分组积分因子法

The Packet Integral Factor Method of First-order Symmetrical Shape Non-exact Differential Equation

对一阶对称形非恰当方程,提出了先将其左端适当分组,再从其中的某一组的积分因子出发的分组积分因子法,并给出了计算该方程的积分因子的公式化结果,从而扩大了求解一阶对称形方程的范围,简化了其求解方法。此外,亦可运用此法来寻求稳定性问题中的李雅普诺夫V函数,进而根据此V函数的定号性来解决某些非线性驻定方程(组)的零解的稳定性问题,对建立医学数学模型或能发挥作用。

This article put forward the packet integral factor method that divided the left side of first-order symmetrical shape non-exact differential equation into groups and then aiming at one of the groups. At the same time, show the formulation result of computing the integral factor of the equation so as to enlarge scope of solving the first-order symmetrical shape non-exact differential equation and simplify the solving mothod. In addition, this mothod can also be used to seek Lyapunov V function in stability problem. Then resolve some stability problem of nonlinear equation（s） zero solution according to the fixed symbol property of V function.