本文给出了解决二种特殊类型的欧拉非齐方程的比较系数法，使这类问题变得简单，并提供了许多方便。
This paper puts forward the comparative coefficient way in solving two special type of Euler equations, which can make it more simple and convenient to use.
常数变易法是求解非齐次线性微分方程的一种有效方法。
Methods of constant variation are an efficient solution to all nonlinear differential equations.
摘要利用由三角级数和幂级数复合构成的函数项级数的有关性质，得到了一类变系数非齐次调和方程边值问题的级数解。
In this paper by using the property of Fourier series a compound series consisting of trigonometric series and power series is established.
给出了常系数非齐次线性微分方程特解的一种新的公式化求解方法。
This paper given the formula of solution for nonhomogeneous linear differential equation with constant coefficients.
本文用有限的二重傅里叶变换解波动方程，热传导方程，拉普拉斯方程以及泊松方程的非齐次边值问题。
In this paper, the finite double Fourier transforms were applied to solve the nonhomogeneous boundary value problems of the wave, heat conduction, Laplace and Poisson equations.
在第三章中，给出了非齐次抽象时滞方程的一些结果。
In the third chapter, some results of inhomogeneous abstract delay equations are given.
讨论了带非负扰动并具有第二类边值的临界非齐次多重调和方程的多解存在性和非存在性。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with the second boundary and with a non-negative perturbation.
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.
由非齐次线性方程组解的结构给出静态工作点的基础解；
Then, the basic solution set of conical magnetic bearing static operation points is given based on the solution structure of linear equation group.
在线性方程组有解判别定理的基础上，给出了一个判定非齐次线性方程组存在全非零解的方法。
On the basis of the solution identification theorem in linear equations, a method is presented to ascertain whether there exists all-nonzero solutions to an inhomogeneous linear equation.
讨论了带非负扰动的临界非齐次多重调和方程多解存在性和非存在性。
This paper deals with the existence and nonexistence of solutions for a critical semilinear polyharmonic equation with a non-negative perturbation.
给出了一个判定齐次线性方程组存在全非零解的充分必要条件。
We present a necessary and sufficient conditions of homogeneous linearity equations existing all-nonzero solution.
提出了一种求解一类非齐次线性常微分方程的精细积分方法，通过该方法可以得到逼近计算机精度的结果。
Precise integration method for a kind of non-homogeneous linear ordinary differential equations is presented. This method can give precise numerical results approaching the exact solution.
给出了可以线性化NLS方程的非齐次线性积分方程。
An inhomogeneous linear integral equation used for the linearization of the NLS equation is proposed.
在原有精细积分法的基础上，对非齐次方程出现奇异矩阵的问题进行探讨。
Based on the original precise integration method, the problem that singular matrix appears in non-homogeneous equation was discussed.
运用并矢代数方法，直接求解时谐电磁场的非齐次波动方程，并给出应用实例。
Using dyadic method, non-homogeneous wave equations of time-harmonic electromagnetic field are solved directly, several examples are calculated.
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.
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.
特别是利用广义格林函数证明了高阶齐次方程存在非平凡解的情况下对应的高阶非齐次边值问题存在一解的充要条件。
In particular, we use generalized Green's function to prove that the high-order nonhomogeneous boundary value problem has a solution when the associated homogeneous problem has a nontrivial solution.
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.
该方法对非齐次项属于该类函数的线性常微分方程行之有效。
This method is effective for linear ordinary differential equations whose non-homogeneous term belongs to the set described above.
将非齐次方程转化为齐次方程不仅使问题变得大为简化，同时也减少了数值计算的工作量。
The treatment, by which the non-homogeneous equation was transformed into homogeneous equation, not only simplifies.
采用增广矩阵的方法将非齐次的模型方程化为齐次的形式再求解。
Using the method of augmented matrix, the model equations are changed from nonhomogeneous form to homogeneous form, to be solved.
本文采用求解非齐次方程组的广义黎曼问题解，对模型数值通量计算格式进行了修改。
In hydrodynamics, however, the scheme for numerical flux is constructed from the solution of the generalized Riemann problem in the present research.
利用线性变换，统一给出常系数线性方程齐次通解和非齐次特解解构造定理的简化证明。
Using linear transform, the simple proof for solution of higher order linear differential equations was given.
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.
考虑非齐次波动方程初边值问题的形式级数解的收敛性问题。
The convergence of the formal series solution to the initial boundary value problem for the non-homogeneous wave equation is considered.
本文研究一类高阶线性齐次与非齐次迭代级整函数系数微分方程解的增长性问题。
In this paper, we investigate growth problems of solutions of a type of homogeneous and non-homogeneous higher order linear differential equations with entire coefficients of iterated order.
本文主要讨论直接线性化方法。给出了可以线性化NLS方程的非齐次线性积分方程。
The paper deals with the direct linearization of the NLS equation. An inhomogeneous linear integral equation used for the linearization of the NLS equation is proposed.
在线性方程组有解判别定理的基础上，给出了一个判定非齐次线性方程组存在全非零解的方法。
Homogeneous linear equations of n-variables have the non-zero solutions when the rank of its matrix is less than n.
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