general integral

With proper method of variable substitution, the soluble method to two kinds of inegrable equation of Riccati form is found, and the general integral expressions are given.

利用适当的变量代换法 ,找到了两类可积的Riccati型方程的求解方法 ,并给出了通积分的表达式。

It offers a wider kind of Abel differential equations,gives the criterion and expression of general integral on them.

提出一类更广泛的Abel型微分方程,给出可积的判据,提供通积分的表达形式,扩充微分方程的可积类型,推广相关文献的结论。

Some sufficient condition for Riccati equation y′=p(x)y2+q(x)y+r(x) and its related general integral are given in this paper.

给出Riccati方程y′=p(x)y2+q(x)y+r(x)求积法的若干充分条件及其对应的通积分。

By using variant transform and elementary integrals to discuss the integral conditions of Riccati differential equations,the sufficient conditions and integral solutions for some Riccati equations are obtained.

利用变量变换和初等积分法来研究Riccati方程的可积性条件,得到了一些Riccati方程可积的充分条件及其通积分。

Some integral sufficient conditions and the integral solutions under these conditions for Riccati equations are obtained.

得到了R iccati方程的一些可积的充分条件及其在这些条件下的通积分,此结果包含了已有文献中的一些结论,最后给出定理应用的例子。

The integral solution of the equationof Riccati type f′(y) d y d x=p(x)f\+2(y)+Q(x)f(y)+R(x)e ∫Q(x) d x is given, under the condition:p(x)e ∫Q(x) d x =21∫R(x) d x ′.

给出 Riccati型方程 :f′(y) dydx=p(x) f 2 (y) +Q(x) f (y) +R(x) e∫Q( x) dx在条件 p(x) e∫Q( x) dx=21 ∫R(x) dx′下的通积分 ,由此 ,得到若干类 Riccati方程的通积

A class of Abel equation of is genrealizationed and general solution of some Riccati equation is derived.

把文 [1]中的一类Abel方程进行推广 ,并由些推出若干可积的Riccati方程的通积

And then using the method of integral, general integral formula can be obtained, so that the integrability of original equations can be proved.

采用函数迭代法,给出一个引理,提出三类新的高阶非线性常微分方程,反复利用函数的迭代使之转化为微分方程组的求解,再应用积分法,以获得原微分方程的通积分公式,从而论证了方程的可积性,直接运用通积分公式,使得求解相应方程的解的过程大为简化。

This paper has found general integral formulas of some types of two - order nonlinear ordinary differential equations by first integral.

本文对几类二阶非线性常微分方程，利用首次积分求得了其通积分公式。

The Integrable Criterions and Its General Integral of a Gertain Sort of Ordinary Differential Equations;

某类常微分方程的可积判据及其通积分

Integral Criterion of One Kind of Second-Orden Ouaclratic Equation And Reduction of Its Integrals to Common Denominaton;

一类二阶二次微分方程的可积判据及其通积分

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

Formula of General Solution to Some Kinds of Third-Order Nonlinear Differential Equations;

几类三阶非线性微分方程的通解(通积分)公式

Types of Transformable Homogeneous Differential Equations & Solution Seeking of Integrals;

可化为齐次微分方程的类型及其通积分

The General Integral of the Original Differential Equation and Making the Formule for Elementary Transcendental Function;

微分方程的通积分与初等超越函数公式的推导

ordinary integral element

寻常[通常]积分元(素)

The solutions are obtained utilizing the integration of properly weighted centres of dilatation over the volume occupied by the body.

通过体积元素积分得到的调和势函数通过椭圆积分及其导数表示。

Total load was then obtained by graphical or numerical integration.

然后，通过图解积分或数值积分可求得总载荷。

special frequent user bonus [personalized Octopus card user]

常客特别积分优惠〔个人八达通卡〕

The Study of General Integral Service Development for X Telecommunication Company;

X省电信公司通用积分业务开发研究

Prediction of volume of distribution values in human using immobilized artificial membrane partitioning,the ionized fraction of compound and plasma protein binding data

高通量筛选药物的人体稳态分布容积

Analysis of Application of Turbo Product Codes in Satellite Communication

Turbo乘积码在卫星通信中的应用分析

Applying the formula, traffic continuity equation in integral calculus form is obtained.

应用全导数的积分公式建立了积分形式的交通流连续性方程。

To deposit(a dissolved or suspended substance) on an electrode by electrolysis.

电解淀积通过电解使（分解或悬浮物质）淀积在电极上

The“ vigilantes” in the market are supposedly alert to any inflationary threat.

按理，市场中的“积极分子”会提防任何通胀威胁。

A common purely mechanical integrator is the disk-roller type.

通用的纯粹机械的积分器是圆盘滚柱型。

Distribution Features of Nutrient and Flux between the Sediment and Water Interface of East China Sea and Yellow Sea;

东、黄海营养盐的分布和沉积物—水界面交换通量