摘要
由著名的Bernoulli微分方程引进了非齐次Bernoulli方程的概念.在一定的条件下通过函数的线性拓扑变换将非齐次Bernoulli方程化为变量分离方程,得到一个新的、实用的可积定理.熟知的一阶线性微分方程、Bernoulli方程及著名的Riccati方程、Appel方程的一些经典的可积性结果都是这定理的特例.从而扩大了常微分方程封闭求积的范围.
The concept of nonhomogeneous Bernoulli equation is introduced from Bernoulli equation, and it is turned into variable seperatable equation by linear topological transformation of unknown function under certain conditions,thus,a practical integrable theorem is obtained.Some classical integrable results of the famous Riccati equation and Appel equation are special ones of this theorem.So,the closed integrated range of ordinary differential equation is expanded.
出处
《纺织高校基础科学学报》
CAS
2002年第4期301-305,共5页
Basic Sciences Journal of Textile Universities
关键词
可积定理
BERNOULLI方程
非齐次微分方程
证明
homogeneous Bernoulli equation
non-homogeneous Bernoulli equation
integrable sufficient condition
general solution
