函数变换法在求解Bernoulli方程中的应用  

Application of the function transform method in solving Bernoulli equation

作　　者：田宝单[1] 

机构地区：[1]西南科技大学理学院,四川绵阳621010

出　　处：《高师理科学刊》2008年第6期10-12,共3页Journal of Science of Teachers＇College and University

基　　金：西南科技大学教改项目(21907xn01-57)

摘　　要：Bernoulli方程是《常微分方程》中的一个重要非线性方程,在分析现有参考文献对Bernoulli方程解法研究的基础上,提出了一种新的方法——函数变换法.通过实例说明该方法的可行性,同时这种方法也对一阶线性非齐次微分方程同样适用,并且还为求解某些线性(甚至非线性)偏微分方程提供一些有价值的研究思路.Bernoulli equation is one of the most important nonlinear equations in Ordinary differential equation. By analyzing the methods of solving this kind of equation sufficiently in the recent research, derived a new method, function transform method, and proved the feasibility of this method is proved by example. At the same time, pointed out that this method is also applicable for the non-homogeneous linear differential equation of first order. Moreover, this method provides valuable means for solving some certain of LPDEs （ even NLPDEs ）.

关 键 词：BERNOULLI方程 常数变易法 积分因子法 变量代换法 函数变换法 

分 类 号：O175.1[理学—数学]