1) first-order implicit ordinary differential equations
一阶隐微分方程
2) first order ordinary differential equation
一阶常微分方程
1.
The solution of first order ordinary differential equation with the integral factor of a product form
一阶常微分方程具有一种乘积形式积分因子的求解
2.
Existence and application of two integrating factors on first order ordinary differential equation
探讨一阶常微分方程两种积分因子的存在性及其应用
3.
Essentially,the opposite reaction kinetics process is a process of resolving the first order ordinary differential equation.
对峙反应动力学过程,其实质是一个求解一阶常微分方程的过程。
3) differential equation of first order
一阶微分方程
1.
In this article, a general soution is given to the inteqral divisor of the differential equation of first order by applying the necessary and sufficient condition of the total differential equatio
应用全微积分方程的充要条件给出了求一阶微分方程积分困于较为一般的方法。
2.
It is shown that the common method of integrating factor of differential equation of first order is given.
为寻找一阶微分方程的积分因子提供了一个一般方法。
4) first order differential equations
一阶微分方程组
1.
In this paper,We make an elementary transfomation to some special Riccati equations,get the second order differential equation or first order differential equations,after that get the special solution of the Riccati equation with the help of special solution of the second order differential equation or first order differential equations,or formula method and observation trial method.
通过对一般Riccati方程进行初等变换,使之变为特殊的Riccati方程,然后利用公式、观察实验,或利用二阶微分方程的特解,或利用一阶微分方程组的特解等方法,求得这些Riccati方程的特解。
5) first order differential equation
一阶微分方程
1.
In this paper,we discuss Osgood condition further,then we have the simplified method to judge the unicity of zero solution about first order differential equation,this bring large convenient to judge the unicity of zero solution about first order differential equation.
一阶微分方程解的存在唯一性定理是在不解出方程的情况下判断初值问题的解是否存在且唯一。
2.
Regarding seeking solution of three kinds of first order differential equations,usually the reference book introduces some methods of looking for integral factor ,then transforms integral factor into full differential equation ,finally through which the solutien is found.
文献对三类一阶微分方程的求解 ,采用先找积分因子 ,再利用积分因子转化为全微分方程 ,然后按全微分方程的求解方法求解 ,其过程较繁复 。
6) first-order partial differential equation
一阶偏微分方程
1.
As the foundation of his first-order partial differential equation theory,Lagrange s definition plays an important role in his general integral theory.
从微观角度看,拉格朗日基于欧拉的定义,在用"常数变易法"探讨一阶偏微分方程积分的过程中受到启发,萌生了其积分"完全性"的新思想,并把这种新思想运用于常微分方程的研究,成功解释了奇解,在此基础上提出了一阶偏微分方程完全积分的新定义,因此拉格朗日完全积分的新定义是"常数变易法"和微分方程奇解现象共同诱发的产物。
补充资料：二阶线性齐次微分方程
二阶线性微分方程的一般形式为
ay"+by'+cy=f(1)
其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为
ay"+by'+cy=0（2）
称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条