摘要
根据一类二阶变系数非线性微分方程的特点,利用降阶法,给出了求其通解的一种简便方法,并得到了其通解公式,并在特殊情形下得到一系列可积的二阶变系数非齐次线性微分方程及其通解公式,进一步丰富了二阶变系数线性微分方程的可积理论.
According to characteristics of the second order nonlinear differential equations with variable coefficients,the reduced-order method has been used;and then an easy way to find the general solution is given;meanwhile,the general solution formula has been obtained.Finally,a series of integrable second-order variable coefficient non-homogeneous linear differential equations and general solution formula in special circumstances has been received;furthermore the integrable theory of the second-order linear differential equation with variable coefficients has been enriched.
出处
《三峡大学学报（自然科学版）》
CAS
2011年第5期96-98,共3页
Journal of China Three Gorges University：Natural Sciences
基金
陕西省教育厅科研计划项目(2010JK400)
宝鸡文理学院重点科研项目(ZK1014)
关键词
非线性微分方程
降阶法
通解
nonlinear differential equations
reduced-order method
general solution
