1、常微分方程第二次作業(yè)第1章 初等積分法 1求解下列方程（1） （2）（3） （4）（5） （6）（7） （8）2求拋物線族的正交軌線3求曲線族的正交軌線，其中為參數(shù)4求一曲線使其上每一點(diǎn)的切線斜率為該點(diǎn)橫坐標(biāo)的2倍，且通過點(diǎn)5人工繁殖細(xì)菌，其增長速度和當(dāng)時(shí)的細(xì)菌數(shù)成正比（1）如果過4小時(shí)的細(xì)菌數(shù)即為原細(xì)菌數(shù)的2倍，那么經(jīng)過12小時(shí)應(yīng)有多少？（2）如果在3小時(shí)的時(shí)候，有細(xì)菌數(shù)個，在5小時(shí)的時(shí)候有個，那么在開始時(shí)有多少細(xì)菌？6重為100kg的物體，在與水平面成30的斜面上由靜止?fàn)顟B(tài)下滑，如果不計(jì)磨擦，試求：（1）物體運(yùn)動的微分方程；（2）求5 s后物體下滑的距離，以及此時(shí)的速度和加速度第2章 基本

2、定理1試畫出下列各方程的積分曲線圖：（1）（為常數(shù)） （2）（3） （4）（5）2試判斷方程在區(qū)域（1） （2）上是否滿足定理2.1的條件？3判斷下列方程在什么樣的區(qū)域上保證初值解存在且惟一？（1） （2）（3） （4）4討論方程在怎樣的區(qū)域中滿足定理2.2的條件并求通過的一切解5試用逐次逼近法方程求滿足初值條件的近似解：，6試證明：對于任意的及滿足條件的，方程的解在上存在7指出方程的每一個解的最大存在區(qū)間，以及當(dāng)趨于這區(qū)間的右端點(diǎn)時(shí)解的性狀8設(shè)在整個平面上連續(xù)有界，對有連續(xù)偏導(dǎo)數(shù)，試證明方程的任一解在區(qū)間上有定義9判斷下列方程是否有奇解？如果有奇解，求出奇解，并作圖（1） （2）（3）10求

3、一曲線，具有如下性質(zhì)：曲線上任一點(diǎn)的切線，在軸上的截距之和為111求一曲線，此曲線的任一切線在兩個坐標(biāo)軸間的線段長等于常數(shù)參考答案第1章 初等積分法1718節(jié)作業(yè)1（1） （2）（3） （4）（5） （6）（7） （8）52 34 5（1）8倍， （2）個6（1）略 （2）時(shí)，第2章 基本定理1 （略）2（1）不滿足 （2）滿足3（1）整個xoy平面 （2）整個xoy平面（3）除y軸x = 0外的整個xoy平面 （4）除x軸y = 0外的整個xoy平面4對，5，6提示：和是解 7提示：是解8見學(xué)習(xí)指導(dǎo)典型例題的例39（1）有， （2）無 （3）有，10 11選做作業(yè) 一、填空題1. 若在(-，

4、+)上連續(xù)，則方程的任一非零解( )與x軸相交.2. 方程滿足解的存在唯一性定理?xiàng)l件的區(qū)域是（ ）3. 連續(xù)是保證方程初值解唯一的( )條件.4. 方程+ ysinx = ex的任一解的存在區(qū)間必是( )二、單選題1. 方程過點(diǎn)(0，0)的解為，此解的存在區(qū)間是( ).（a）（，） （b）（c）（，0） （d）0，2. 方程滿足解的存在唯一性定理?xiàng)l件的區(qū)域是( ).(a)全平面； (b)y0的上半平面；(c)y0的下半平面； (d)除去x軸的全平面.3. 方程是否存在奇解( ).(a)無奇解； (b)有奇解；(c)不一定； (d)可能有奇解.4.函數(shù)f(x, y)=y對y是否滿足李普希茲條件(

5、 ).(a)不滿足； (b)滿足.(c)可能滿足； (d)可能不滿足參考答案： 一、填空題 1.不能 2.滿足的平面區(qū)域 3.充分 4.（） 二、單選題待添加的隱藏文字內(nèi)容3 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 - s

6、aid he wanted 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 wi

7、th fines. you 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 vil

8、lains we have 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 celebra

9、tions and will 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 proc

10、eedings against 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

11、russian side 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

12、mph, with no 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

13、higher than 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 wil

14、l slowly step 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 b

15、e like he is 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 wi

16、ll not be enough 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