1) linear homogeneous differential equation
齐线性微分方程
1.
For the high-order linear homogeneous differential equations with variable coefficients,there has no unified way to get the functional expression of their non-zero solutions,so it is very necessary to study the property of non-zero solutions macroscopically.
对于高阶的变系数齐线性微分方程,我们没有统一的方法可以求出其所有非零解的函数表达式,因此从宏观上研究其非零解的性质是非常必要的。
2) nonhomogeneous linear differential equation
非齐线性微分方程
1.
Method of substitution of constants is an important method for solving nonhomogeneous linear differential equations.
常数变易法是求解非齐线性微分方程(组)的一种重要方法。
3) Nonhomogeneous linear ordinary differential equation
非齐线性常微分方程
1.
The paper introduces basic sets of solutions for nonhomogeneous linear ordinary differential equations and proves that the general solutions of such equations consist of all convex linear combinations of any basic set of solutions.
引进了非齐线性常微分方程的基本解组,证明了非齐线性常微分方程的通解由其基本解组的所有凸线性组合构成,由此给出了非齐线性常微分方程通解的又一表达形式。
4) non homogeneous and linear differential equations
非齐次线性微分方程组
1.
A method to solve non homogeneous and linear differential equations by homogenization high precision direct integration (HHPD P) was proposed.
根据函数分段插值逼近的思想 ,在一个积分步长内用多项式近似表示方程的非齐次项 ,提出了一种原理简单、实施容易的求解非齐次线性微分方程组的新型齐次扩容精细积分法 ,该方法不涉及矩阵的求逆运算 ,不需要计算傅里叶级数展开系数的振荡函数积分 ,且在一个积分步长内只求解一个相应的齐次扩容微分方程组 ,因而本方法和已有的同类方法相比具有更高的计算精度和效率 ,数值算例表明了该方法的有效
5) homogeneous linear differential equation
齐次线性微分方程
1.
Several types which can be reduced for third order homogeneous linear differential equation with varied coefficient;
几种可降阶的三阶变系数齐次线性微分方程类型
2.
In this paper we investigate the growth of solutions of second order homogeneous linear differential equations f″+Ae pf′+Be Qf=0 where P,Q are polynomials with different degrees,A,B are entire functions,their orders are less than orders of e p,e Q respectively.
该文研究了二阶齐次线性微分方程ｆ″＋Ａｅｐｆ′＋ＢｅＱｆ＝０的解的增长性，其中Ｐ，Ｑ为次数不同的多项式，Ａ，Ｂ为级分别小于ｅＰ，ｅＱ的级的整函数。
6) homogeneous linear ordinary differential equation
齐次线性常微分方程
1.
In this paper,the variational stability of bounded variation solutions to homogeneous linear ordinary differential equations are disscussed by using Henstock integral and Lyapunov function,the Lyapunov type theories for variation stability and variational-asymptotically stability of bounded variation solutions are established.
利用Henstock积分和Lyapunov函数,讨论了齐次线性常微分方程有界变差解的稳定性,建立了有界变差解的变差稳定性和变差渐近稳定性的Lyapunov型定理。
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