常系数线性微分方程

In this paper, we study an approximate solution of the second-order linear ordinary differential equations with variable coefficients .

本文研究了二阶变系数线性常微分方程的一种近似求解方法。

Movement stabilization criterion of nonlinear relative rotation system was obtained by transferring the fundamental matrix of the solution of the ordinary differential equation to Jordan canonical .

利用一类周期性变系数线性常微分方程解的基本矩阵的Jordan形，分析一类非线性相对转动系统扭转的运动稳定性，从而得到非线性相对转动周期系统的运动稳定准则。

An important case is the linear homogeneous second-order differential equation with constant coefficients.

一种重要的情形是常系数二阶线性齐次微分方程。

This paper discusses the broad-sense relation between solution and coefficient of some special kinds of second order variable coefficient and homogeneous linear differential equation,and have a try of giving a general form of common solution and the coefficient decision formula of special solution.

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 first is refered to the vibration model with retardation for the market equilibrium price, where the knowledge of the second order linear ordinary differential equation is used.

第一个是研究市场调节下平衡价格的阻尼振荡模型，使用了二阶线性常系数微分方程的课程知识；第二个是在引进社会福利因素时商品的最优定价模型，使用了定积分和微分法的课程知识。

The first is refered to the vibration model with retardation for the market equilibrium price, where the knowledge of the second order linear ordinary differential equation is used. The second is refered to the optimal pricing model of the price under the frame of the social welfare, where the concept of the definite integral is exploited.

第一个是研究市场调节下平衡价格的阻尼振荡模型，使用了二阶线性常系数微分方程的课程知识；第二个是在引进社会福利因素时商品的最优定价模型，使用了定积分和微分法的课程知识。

For overcome nonlinear terms of any degree in the equation, we made a proper transformation according to the structure of the equation at first, make the equations into ordinary differential equation. Then solve the ordinary differential equation exactly, by auxiliary functions method and undetermined the coefficient method and algebraic computer system Mathematica.

为了克服方程中非线性项的任意次幂，我们采用的方法是首先根据方程的特点，做适当的变换，使原问题转化为常微分方程的问题，其次对该常微分方程再进行各类变换，如辅助函数法以及待定系数法……。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。