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integrable sufficient condition
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  可积
     In this paper,the concept of characteristic equation is introduced into one kind of Riccati differential equation, a practical integrable sufficient condition of this kind of equation is given. And so a new integrable type of Riccati equation is obtained.
     对一类Riccati微分方程引入特征方程的概念 ,给出了该类方程一个实用的可积充分判据 ,从而得到了Riccati方程的一个新的可积
短句来源
     ConclusionThe integrable sufficient condition obtained by linear transform of unknown function is a general integrability result of this equation.
     结论 得到的可积充分条件是利用未知函数的线性变换来研究该方程可积性的一个一般性结果。
短句来源
     The solvable of second order linear non-homogeneous differential equation which in important in (theory) and practice is studied. The concept of characteristic equation system is leaded into second order linear differential equation. Thus a new practical integrable sufficient condition that variable coefficient second order linear non-homogeneous differential equation and analytic expression fomula of the general solution is given.
     研究在理论上和应用上占有重要地位的二阶线性非齐次微分方程的解法,引入特征方程组的概念,得到二阶变系数线性非齐次微分方程的一个新的、实用的可积充分判据,并给出了其通解的解析表达式,推广了经典的二阶常系数线性非齐次微分方程的解法.
短句来源
     In this paper, intrcduces two concepts of dual equation and characteristic constant into famous Riccati equation and obtain a new practical integrable sufficient condition. Thus a series of new integrable typs are derived. So, we extend the former integrable results of Riccati equation.
     对著名的Riccati方程引入伴随方程和特征常数的概念,得到了该方程一个新的、实用的可积充分条件,导出了一系列新的可积类型,推广了前人关于Riccati方程的一些可积结果,同时还纠正了前人某些结果的错误。
短句来源
     The author indicates the exis ent wrong of integrable sufficient condition obtained by D. Mirrinovitch in 1938 and quoted all along by successors in the teaching and the scien ific reseach, and presents a general integrable sufficient condition.
     Mirrinovitch于1938年得出并被后来在教学科研中一直引用的可积充分条件所存在的错误,给出了一个普遍的可积充分条件。
短句来源
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  可积充分判据
     In this paper,the concept of characteristic equation is introduced into one kind of Riccati differential equation, a practical integrable sufficient condition of this kind of equation is given. And so a new integrable type of Riccati equation is obtained.
     对一类Riccati微分方程引入特征方程的概念 ,给出了该类方程一个实用的可积充分判据 ,从而得到了Riccati方程的一个新的可积类
短句来源
     The solvable of second order linear non-homogeneous differential equation which in important in (theory) and practice is studied. The concept of characteristic equation system is leaded into second order linear differential equation. Thus a new practical integrable sufficient condition that variable coefficient second order linear non-homogeneous differential equation and analytic expression fomula of the general solution is given.
     研究在理论上和应用上占有重要地位的二阶线性非齐次微分方程的解法,引入特征方程组的概念,得到二阶变系数线性非齐次微分方程的一个新的、实用的可积充分判据,并给出了其通解的解析表达式,推广了经典的二阶常系数线性非齐次微分方程的解法.
短句来源
  “integrable sufficient condition”译为未确定词的双语例句
     Studies an integrable question of Pfaff constraint,utilizing the integrable sufficient condition of Pfaff constraint,giving an integrable sufficient conditions of the Euler form as Pfaff constraint-proposition 1,and points out that the inverse-proposition of proposition 1 in general does not hold as proposition 2.Examples are given to explain the applications of proposition 1 and proposition 2.
     研究Pfaff约束可积性问题. 利用Pfaff约束可积的充分条件,给出Pfaff约束可积的Euler形式的充分条件———命题1.指出命题1的逆命题一般并不成立———命题2.举例说明命题1和命题2的应用.
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This Prper gives a united integrable form of the nonlinear ordinary differen, tial eauation stuolied in papers [1] [2] A. integrable sufficient condition and it's universal integral were put forward. Conseauently, We got a new infegra-eble form of nonlinear ordinary differential eguation.

本文给出了文[1]、[2]研究的非线性常微分方程可积类型以统一的形式,提供了可积的充分条件及其通积分,并且推广了文[1]、[2]的有关结论,因而得到了新的非线性常微分方程的可积类型。

Integrable condition of Riccati equation is s udied in this paper. The author indicates the exis ent wrong of integrable sufficient condition obtained by D. Mirrinovitch in 1938 and quoted all along by successors in the teaching and the scien ific reseach, and presents a general integrable sufficient condition.

本文研究Riccati方程的可积情况,指出了由D.Mirrinovitch于1938年得出并被后来在教学科研中一直引用的可积充分条件所存在的错误,给出了一个普遍的可积充分条件。

An integrable sufficient condition of a solt of nonlinear differential equations is proposed in this paper, which generalizes at least some classical integrable typpes, such as first - order linear equation. Bemoulli equahon. From it deriver a series of netw practical integrable resuls and types of foccati equation and second - order linear equation. Moreover, some mistakes in other re-searchers' results are pointed out and corrected.

给出了一类非线性常微分方程的可积充分条件,它至少概括了一阶线性方程、Bernoulli方程等一些古典的可积类型,由它可导出Riccati方程和二阶线性方程的一系列新的、实用的可积性结果和可积类型。纠正了前人某些结果的错误。

 
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