摘要
提出几类非线性微分方程,巧妙地借助线性化法、降阶法、交换变量位置法,将非线性微分方程转化为新的二阶变系数线性微分方程,在一定条件下,给出这几类非线性微分方程的可积性证明,提供了可积的判据及通解的表达式,并列举了实例。
In this paper several types of nonlinear differential equations are investigated and transmuted to new second-order linear variable-coefficient differential equations by employing linear transformation method, order reduction method, and exchange variables method dexterously. The integrability of these nonlinear differential equations are also proved within particular restricts. Then the integrable criterions and expressions of general solutions are given and some samples are suggested.
出处
《云南师范大学学报（自然科学版）》
2005年第5期6-10,共5页
Journal of Yunnan Normal University:Natural Sciences Edition
关键词
非线性微分方程
线性化法
降阶法
交换变量位置法
二阶变系数微分方程
可积判据
通解
nonlinear differential equations
linear transformation method
order reduction method
exchange variables method
second-- order variable-- coefficient differential equations
integrable Criterions
