电大常微分方程第二次作业

1、常微分方程第二次作业第1章 初等积分法 1求解下列方程（1） （2）（3） （4）（5） （6）（7） （8）2求抛物线族的正交轨线3求曲线族的正交轨线，其中为参数4求一曲线使其上每一点的切线斜率为该点横坐标的2倍，且通过点5人工繁殖细菌，其增长速度和当时的细菌数成正比（1）如果过4小时的细菌数即为原细菌数的2倍，那么经过12小时应有多少？（2）如果在3小时的时候，有细菌数个，在5小时的时候有个，那么在开始时有多少细菌？6重为100kg的物体，在与水平面成30的斜面上由静止状态下滑，如果不计磨擦，试求：（1）物体运动的微分方程；（2）求5 s后物体下滑的距离，以及此时的速度和加速度第2章 基本

2、定理1试画出下列各方程的积分曲线图：（1）（为常数） （2）（3） （4）（5）2试判断方程在区域（1） （2）上是否满足定理2.1的条件？3判断下列方程在什么样的区域上保证初值解存在且惟一？（1） （2）（3） （4）4讨论方程在怎样的区域中满足定理2.2的条件并求通过的一切解5试用逐次逼近法方程求满足初值条件的近似解：，6试证明：对于任意的及满足条件的，方程的解在上存在7指出方程的每一个解的最大存在区间，以及当趋于这区间的右端点时解的性状8设在整个平面上连续有界，对有连续偏导数，试证明方程的任一解在区间上有定义9判断下列方程是否有奇解？如果有奇解，求出奇解，并作图（1） （2）（3）10求

3、一曲线，具有如下性质：曲线上任一点的切线，在轴上的截距之和为111求一曲线，此曲线的任一切线在两个坐标轴间的线段长等于常数参考答案第1章 初等积分法1718节作业1（1） （2）（3） （4）（5） （6）（7） （8）52 34 5（1）8倍， （2）个6（1）略 （2）时，第2章 基本定理1 （略）2（1）不满足 （2）满足3（1）整个xoy平面 （2）整个xoy平面（3）除y轴x = 0外的整个xoy平面 （4）除x轴y = 0外的整个xoy平面4对，5，6提示：和是解 7提示：是解8见学习指导典型例题的例39（1）有， （2）无 （3）有，10 11选做作业 一、填空题1. 若在(-，

4、+)上连续，则方程的任一非零解( )与x轴相交.2. 方程满足解的存在唯一性定理条件的区域是（ ）3. 连续是保证方程初值解唯一的( )条件.4. 方程+ ysinx = ex的任一解的存在区间必是( )二、单选题1. 方程过点(0，0)的解为，此解的存在区间是( ).（a）（，） （b）（c）（，0） （d）0，2. 方程满足解的存在唯一性定理条件的区域是( ).(a)全平面； (b)y0的上半平面；(c)y0的下半平面； (d)除去x轴的全平面.3. 方程是否存在奇解( ).(a)无奇解； (b)有奇解；(c)不一定； (d)可能有奇解.4.函数f(x, y)=y对y是否满足李普希兹条件(

5、 ).(a)不满足； (b)满足.(c)可能满足； (d)可能不满足参考答案： 一、填空题 1.不能 2.满足的平面区域 3.充分 4.（） 二、单选题 1b 2d 3a 4bif we dont do that it will go on and go on. we have to stop it; we need the courage to do it.his comments came hours after fifa vice-president jeffrey webb - also in london for the fas celebrations - said he want

6、ed to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated by the ivorian and the british media.blatter, 77, said: it has been decided by the fifa congress that it is a nonsense for racism to be dealt with with fines. y

7、ou can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is against the spirit of football and against the visiting team. it is all nonsense.we can do something better to fight racism and discrimination.this is one of the villains we ha

8、ve today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and w

9、ill attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings aga

10、inst cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian sid

11、e added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with n

12、o precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than

13、 the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly st

14、ep out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants to land on, but not too hard. still, hell be traveling fast, so despite the distance, it will not be like diving into the deep end of a pool. it will be like he i

15、s diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 690 mph (1,110 kph) - in less than 40 seconds. like hitting the top of the water, he will begin to slow as he approaches the more dense air closer to earth. but this will not be e

16、nough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute that can be deployed to slow him down. his team hopes its not needed. instead, he plans to deploy his 270-square-foot (25-square-meter) main chute at an altitude of around 5,000 feet (1,524 meters).in order to deploy this chute successfully, he will have to slow to 172 mph (277 kph). he will have a reserve parachute that will open automatically