A rediscussion on integrability condition of Riccati equation;
关于Riccati方程的可积条件研究的再讨论
That is,integrability condition of equation y′=P(x)y~n+Q(x)y+R(x) is not(R=K′Pe~(n∫(Q-β D)d x))(K′,β are constants) but Q-1[]n\sR′[]R\s-P′[]P\sPR~(n-1)=τ(τ is a constant).
指出《科学通报》1998年第1期《Riccati微分方程一个新的可积条件》中的错误并给出正确结论,即方程y′=P(x)yn+Q(x)y+R(x)的可积条件不是R=K′Pe∫n(Q-βD)dx(K′,β为常数),而是Q-1nRR′-PP′nPRn-1=τ(τ为常数);给出了满足这一条件的方程的通积分;推广了该方程原有的可积条件R=KPe∫nQdx(K为常数)。
By using the proof of integrable conditions of linear nonholonomic systems for reference,the integrable conditions of nonlinear nonholonomic systems were proved in this paper.
通过对非完整约束方程的变分式应用可积性条件 ,推导出Chetaev条件 ;并且指出 ,如此应用可积条件 ,不会使非完整系统变为完整系统 。
We make use of the integrable condition in Standard Form improving the Wu Differential Characteristic Chain Algorithms.
本文主要利用标准型中的可积条件算法,对吴微分特征列法做了一些改进;并在计算机上,利用Mathematica工具软件,用改进的方法,对偏微分方程组进行了化简。
And,the integrability conditions and general solution formula of two types second-order linear differential equation were given.
利用高阶导数的恒等式,得出变系数二阶线性微分方程具有积分形式的通解公式;其次给出两类二阶线性微分方程的可积条件与通解公式。
This papre gives Riccati equation integrable conditions and classes by its invariant, and applies its solution on other differential equations.
利用Ricati方程的不变量，给出R氏方程的可积条件及可积类型，并应用结果解决其它微分方
Some new integral conditions of Riccati differential equation;
Riccati方程的一些新的可积性条件
The integral conditions of riccati differential equation;
Riccati方程的可积性条件
The Integrable Condition for Riccati Equation;
关于Riccati方程的可积条件
Discussion on the Text of《Integral Conditions and Representatives of Riccati Equation》
Riccati方程的可积条件及通积分的讨论研究
Integrability Conditions of A Class of Third-order Nonlinear Differential Equation;
一类三阶非线性微分方程的可积条件
Integral Condition and Application on Complex Coefficient Riccati Equation;
复系数Riccati方程的可积条件及其应用
A New Integrational Condition for Riccati Formula;
Riccati方程一个新的可积条件
Integrable Condition and Its Computer Determination for A Kind of Special Abel Equation
一类特殊阿贝尔方程的可积条件及计算机判定
On Integrability Conditions of Generalized Riccati Equation--To discuss about it with Mr.Zhao Linlong;
关于广义Riccati方程的可积条件——与赵临龙先生商榷
A New Integrable Condition of Third Order Nonlinear Differential Equation;
三阶非线性微分方程一个新的可积条件
Conditions of Term by Term Integration Sequence of Integrable functions on Finite Interval;
有限区间上广义可积函数列逐项积分的条件
A Condition of Term by Term Integration Sequence of Integrable Functions on Infinite Interval;
无穷区间上可积函数列逐项积分的条件
Two Conditions of the Integrability for Almost Kaehler Manifolds;
近Kaehler流形的两个可积性条件
A Sufficient Condition of Integrability for Riccati Equation;
Riccati方程可积的一个充分条件
The new solution to the sufficient condition of integrability for a old Riccati equation;
关于Riccati方程可积的充分条件的探讨
Some Sufficient Conditions of Riccati Equation are Integrable;
Riccati方程可积的若干充分条件
Some Efficient Integrabel Conditions to Extend Riccati Equation;
推广的Riccati方程可积的若干充分条件
The Integral Conditions of Riccati Equation and its Application
Riccati方程的可积性条件及应用
Extension of Integral Conditions of Riccati Differential Equation
一类Riccati方程可积性条件的推广
A Necessary and Sufficient Condition for Riemannian Integrability of the Limit Funtion of a Sequence of Riemann Integrable Functions
黎曼可积函数序列的极限函数为黎曼可积的充要条件——黎曼积分号下取极限的充要条件