余函数（齐次解）对应于暂态，特解对应于稳态。
Eg. The complementary function corresponds to the transient, and the particular solution to the steady state.
这样，轴对称正交异性圆环壳的齐次解第一次有了达到薄壳理论精度的完全的渐近展开。
Thus, the fully asymptotic expansion of the homogeneous solution within the accuracy of theory of thin shells is obtained.
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.
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.
应用生成函数的方法求出了常系数非齐次线性递推式的显式解。
This paper gives an explicit solution to linear non-homogeneous recurrence relations with constant coefficients by means of generating function.
本文利用齐次平衡法并借助数学给出它新的多孤子解。
In this paper, by using the homogeneous balance method and Mathematica, we have obtained new multisoliton solutions of this equations.
权函数是得自对应的齐次微分方程的一般解和完备系。
The weighted functions are obtained based on the use of completed systems of general solution of the corresponding homogeneous 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.
本文研究了线性递推方程解的结构以及常系数线性齐次递推方程解法。
In this paper, we study the structure of the linear recursion equation and get the solution to the constant coefficient linear homogeneous recursion equation.
给出了求齐次线性方程组正交的基础解系的一个简便方法和一个应用实例。
A simple method for the orthogonal fundamental solution of homogeneous linear equation system and the example in its application are given.
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.
利用齐次线性方程组解的理论讨论矩阵的秩，给出几个关于矩阵秩的著名不等式的证明，并证明了两个命题。
The article discusses rank of a matrix by the solution theorem of system of homogeneous linear equations, and proves several famous inequalities and two propositions on rank of a matrix.
分别给出具有第三类齐次边条件的混合问题基本解以及具有零初始条件的混合问题基本解。
The fundamental solution of the mixed problem with the third kind homogeneous boundary condition and that with the zero initial condition are given respectively.
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.
建立了角台机构的反解方程，通过确定结构约束和齐次变换矩阵，解得角台机构的三个移动副输入参数。
Then it builds the equations for inverse problem and obtains the three input parameters according to the structure constraints and homogeneous transforming matrixes.
基于齐次平衡法的思想，利用多项式展开法解得了具有色散项的长波方程组的精确解。
The exact solutions to dispersive long-wave equations are obtained by a polynomial expansion method based on the idea of the homogeneous balance method.
通过分析发现，预应力设计的结果实际上就是一个齐次线性方程组的解空间。
The result of the prestress design is actually the solution space of a homogeneous linear equation set.
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.
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.
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.
机器人位置问题正解采用齐次变换矩阵法解算，逆解采用只保证位置的插值算法。
The positive algorithm of robot positions is solved by the same power transformation matrix method, while the negative algorithm adopts interpolating method ensuring the position only.
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.
本文用齐次平衡方法求出了哈密顿振幅方程的精确解。
The validity of homogeneous balance method for solving differential equation was shown by solving a new Hamilton amplitude equation.
使用齐次平衡方法，得到了（2+1）维破裂孤子方程的一些新多孤子解。
Using the extension homogeneous balance method, we have obtain some new special types of soliton solutions of the (2 + 1) - dimensional breaking soliton equation.
将行列式的值、矩阵的秩、齐次线性方程组的解等知识运用于向量组线性相关性判定，归纳出六种判定向量组线性相关性的方法。
The judging methods of the vectors group related dependence from determinant values, rank of matrix, solution of system of linear equations etc were studied.
运用齐次化同伦连续法给出了两组非线性设计方程组的数值解。
By using the generalized homotopy iteration method, the sets of nonlinear synthesis equations were solved, and the whole numerical solutions were given out as a result.
第六章研究了齐次平衡法新的应用，把它应用到WBK方程上去得到了许多新的精确解。
In Chapter 6, we study new applications of homogenous balance method and apply the method to WBK equation and obtain many new exact solutions.
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.
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.
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