摘要
通过对一阶常微分方程中的齐次方程的推广形式——齐次型方程进行研究,并将齐次方程"变量变换"法求解过程推广应用到齐次型方程,从而证明了齐次型方程是可积方程,得到了一阶微分方程的几种新的可积类型,其中包括部分黎卡提方程和贝努利方程.
This paper studies the equation of a homogeneous type, which is the generalized form of homogenous equation in the first order differential equation. The procedure of solving the homogenous differential equation by a variable transformation method is generalized to solve equations of the homogenous type. Meanwhile, the author proves that the equation of a homogenous type is an integrable equation and gets some new integrable differential equations of the first order, including Reccati equation and Bernoulli equation.
出处
《湖州师范学院学报》
2009年第2期122-126,共5页
Journal of Huzhou University
关键词
齐次方程
齐次型方程
变量变换法
可积方程[1
homogeneous equation
equation of homogeneous type
variable transformation
integrable equation
