1) total differential equation
全微分方程
1.
his paper gives a method of obtaining the general solution of the equations to be U(x,y) = C through properly decomposing M(x,y) and N(x,y) in a total differential equation M(x,y)dx + N(x,y)dy = 0, and having indefinite integrals to get the binary function U(x, y).
本文给出了通过适当分解全微分方程Ｍ（ｘ，ｙ）ｄｘ＋Ｎ（ｘ，ｙ）ｄｙ＝０中的Ｍ（ｘ，ｙ）和Ｎ（ｘ，ｙ），然后作不定积分求出二元函数Ｕ（ｘ，ｙ），从而求得方程通解Ｕ（ｘ，ｙ）＝Ｃ的一种方法。
2.
By means of the conditions of total differential equation,in this paper are given the integral factor and general solution of one kind of differential equation and are obtained the differential equations that satisfy the unknown functions in some of total differential equations, thus are found the unknown functions and their general solutions.
利用全微分方程的条件 ,给出一类微分方程的积分因子及通解公式 ,得出几类全微分方程中未知函数所满足的微分方程 ,获得未知函数及全微分方程的通
2) complete differential equation
全微分方程
1.
Transforming first order differential equation to complete differential equation by the way of integrating factors is an important means to seek solution for differential equations.
采用积分因子方法将一阶微分方程转化为全微分方程是求解微分方程一个重要手段,讨论了积分因子存在的充要条件及确定若干特殊类型积分因子的准则;通过实例来说明准则的应用方法。
2.
By means of the conditions of complete differential equation, this paper gives the integrate factor and general solution to one kind of differential equations, and gets the second-order linear differential equation for unknown function of one kind of complete differential equations and the general solution to complete differential equation.
利用全微分方程的条件,给出一类微分方程的积分因子及通解公式,得出一类全微分方程 中未知函数所满足的二阶线性微分方程,获得未知函数及全微分方程的通解。
3.
This paper discusses one type of complete differential equation and by means of its necessary and sufficient conditions, we obtain second-order linean differential equation whose conditions the unkown function should meet, and the expression of general solution to function and complete differential equation.
讨论了一更全做个方程的求解问题，利用全微分方程的充要条件什，得出未知函数所应满足的二阶线性微分方程，获得未知函数及全微分方程通解的表达式。
4) exact differential equation
全微分方程
1.
As the first order differential equation M(x,y)dx + N(x,y)dy = 0 is not an exact differential equation,finding its integral factor becomes the key to solve the equation,which is a tough issue.
一阶微分方程M(x,y)dx+N(x,y)dy=0不是全微分方程时,寻找它的积分因子成为求解方程的关键,但又是比较棘手的问题。
5) complet second order linear differential equation
完全二阶线性微分方程
6) totally hyperbolic differential equation
全双曲型微分方程
补充资料：全微分
| 全微分 complete differential 如果二元函数z＝f(x，y)在P(x，y)点的增量Δz＝f(x＋Δx，y＋Δy)－f(x，y) 能表示为Δz＝AΔx＋BΔy＋0(ρ)，其中  ，A、B，是与Δx和Δy无关的常数，0（ρ）表示当ρ→0时比ρ高阶的无穷小量， 即0(ρ)趋于0的速度比ρ趋于0的速度要快，AΔx＋BΔy成为函数增量的主要部分，并且关于Δx、Δy是线性的，则说二元函数z＝f（x，y)Ｔ赑点可微，称AΔx＋BΔy为函数的全微分。记为dz＝AΔx＋BΔy，因自变量的微分等于改变量，所以dz＝Adx＋Bdy。与一元函数所不同之处是，在一元函数中，函数在P点可微与可导是等价的，但对二元函数来说，由可微可推出两个偏导数(见偏导数)存在，但光从两个偏导数存在还不能得出可微的结论。 |
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