本文证明任意阶次磁多极子场力线方程总可以用有限形式解析地表示，并对偶极族和四极族磁多极子场力线的位形给予注记。
In this paper it is pointed out that the equation of field lines of a magnetic multipole with any order and degree can always be analytically expressed in term of finite form.
为了探讨锚泊线一阶运动的影响，本文通过求解非齐次和齐次方程，分别求得相应的二阶锚链阻尼和二阶锚链力。
In order to find the effect of first-order responses of mooring line, the second order mooring line tension and damping were determined by solving the non-homogeneous and homogeneous equations.
讨论了一类二阶强次线性时滞微分方程解的振动性质，建立了三个新的振动性定理。推广和改进了已知的一些结果。
The oscillation of a class of second order strongly sublinear delay differential equations is discussed. Three new theorems are established. The results generalize and improve some known ones.
讨论了一类二阶强次线性时滞微分方程解的振动性质，建立了三个新的振动性定理。
The oscillation of a class of second order strongly sublinear delay differential equations is discussed. Three new theorems are established.
在求解域上，利用迦辽金法，将泊松方程的非齐次部分用一个5阶多项式近似表示，而这些多项式对应的方程特解可以很容易获得。
In the solution domain, thePoisson equation is approximated with the 5-order polynomial using Galerkin method, and the particular solution of the polynomial can be determined easily.
本文利用物理学中常见的热传导理论，形象地阐释了二阶齐次线性偏微分方程的本质。
With the ordinary theory of Heat Exchange in physics this essay visualizes the essence of second-order homogenous linear partial differential equations.
一种重要的情形是常系数二阶线性齐次微分方程。
An important case is the linear homogeneous second-order differential equation with constant coefficients.
讨论了一类二阶强次线性微分方程解的振动性质，获得了三个新的振动性定理，推广和改进了相关文献的结果。
The oscillation for solutions of the class of the second order strongly sublinear differential equation are discussed and three new oscillation theorems are obtained.
给出了变系数二阶齐次线性常微分方程的一种积分形式解和几类变系数二阶齐线性常微分方程的普遍解。
The solutions of interal form and the general solutions of some second order homogeneous linear differential equations with variable coefficient are given.
通过应用高温构件蠕变损伤的随机方程及一次二阶矩理论和方法，对高温构件的概率寿命预测进行了研究。
The probabilistic life prediction of high temperature components was studied by using the stochastic equation of creep damage and simple second-order theory and method of high temperature components.
利用分离变量方法导出了在混合边界条件下的非齐次分数阶扩散-波动方程的解析解。
We derive the analytic solution of the non-homogeneous fractional diffusion-wave equation under the mixed boundary conditions using the method of separation of variables.
第一节介绍了三次矩阵样条函数方法和四次矩阵样条函数方法逼近一阶矩阵线性微分方程的数值解。
Section I describes the numerical solution of first order matrix linear differential equation using the cubic matrix spline function and quartic matrix spline function.
后者由于把一个二阶微分方程的求解转化成为两次积分问题，也使计算过程简化。
For the latter, since we transform the problem to seek to solve the second order differential equation into that of twice integrations, the calculating process is also simple.
二阶常系数非齐次线性微分方程的特解一般都是用“待定系数”法求得的，但求解过程都比较繁琐。
In general, special solution of non-homogeneous linear equation of constant coefficient of the second order is obtained by the method of undetermined coefficient, but it's process is too complicated.
第二节介绍用三次矩阵样条函数方法逼近一阶矩阵非线性微分方程的数值解。
Section II describes the numerical solution of first-order matrix differential non-linear equation using the cubic matrix spline function.
应用多尺度微扰理论，对于弱耦合常数的六次非简谐振子得到了其运动方程的经典和量子情况下的一阶解。
Classical and quantum oscillators of quartic anharmonicity are solved analytically up to the second power of (weak-coupling constant) by using the multiple-scale perturbation theory.
提出了非齐次线性递归方程的降阶公式，并由此导出了常系数非齐次线性递归方程的特解公式。
We give a theoretical basis for special solution of the linear non-homogeneous recursion equation with constant coefficient.
本文给出了一个二阶常系数线性非齐次微分方程的特解公式。
This paper deals with the formula of particular solution to 2-order linear inhomogeneous differential equation with constant coefficients.
探讨了某些特殊类型二阶变系数齐次线性常微分方程的解与系数的广义关系，尝试了从理论上给出通解的一般形式和特解的系数决定式。
The thesis analyzes the relationship between Wronsky determinant and linear equation relativity of function in order to get the common solution determinant of linear differential coefficient equation.
利用常数变易法求解具有实特征根的四阶常系数非齐次线性微分方程，在无需求其特解及基本解组的情况下给出其通解公式，并举例验证公式的适用性。
Demonstrated in this paper is how the Constant-transform method, the typical method for solving differential equations of order one, is used in solving linear differential equations of order three.
利用常数变易法求解具有实特征根的四阶常系数非齐次线性微分方程，在无需求其特解及基本解组的情况下给出其通解公式，并举例验证公式的适用性。
Demonstrated in this paper is how the Constant-transform method, the typical method for solving differential equations of order one, is used in solving linear differential equations of order three.
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