電大常微分方程期末試題A小抄參考

1、得分評卷教師 一、填空題（每空2 分，共16分）。1方程滿足解的存在唯一性定理條件的區(qū)域是2. 方程組的任何一個解的圖象是 維空間中的一條積分曲線.3連續(xù)是保證方程初值唯一的 條件4方程組的奇點的類型是 5方程的通解是 6變量可分離方程的積分因子是 7二階線性齊次微分方程的兩個解,成為其基本解組的充要條件是 8方程的基本解組是 得分評卷教師 二、選擇題（每小題 3 分，共 15分）。9一階線性微分方程的積分因子是（ ）（a） （b） （c） （d）10微分方程是（ ）（a）可分離變量方程 （b）線性方程 （c）全微分方程 （d）貝努利方程11方程x(y21)dx+y(x21)dy=0的所有常數(shù)

2、解是（ ）(a) (b) (c), (d), 12階線性非齊次微分方程的所有解（ ） （a）構(gòu)成一個線性空間 （b）構(gòu)成一個維線性空間 （c）構(gòu)成一個維線性空間 （d）不能構(gòu)成一個線性空間13方程（ ）奇解（a）有一個 （b）有無數(shù)個 （c）只有兩個 （d）無得分評卷教師 三、計算題（每小題8分，共48分）。14求方程的通解15求方程的通解16求方程的通解17求方程的通解18求方程的通解19求方程組的實基本解組得分評卷教師 四、應(yīng)用題（本小題 11 分，共11分）。20（1）求函數(shù)的拉普拉斯變換（2）求初值問題的解得分評卷教師 五、證明題（本小題10分，共10分）。21 證明：對任意及滿足條件

3、的，方程的滿足條件的解在上存在。常微分方程復(fù)習(xí)習(xí)題集一 求解下列一階微分方程1234567891011121314151617二 求解下列微分方程組1. 3. 2. 4. 三 求下列微分方程的通解1. 2. 3. 4. 四 敘述“皮卡存在唯一性定理”，并求下列初值問題1. 2. 的第三次近似解。五 對任意的及滿足條件的，求方程的滿足初值條件的解的最大存在區(qū)間。六 考慮微分方程（1）設(shè)與是它的任意兩個解，試證與的朗斯基行列式恒等于一個常數(shù)；（2）設(shè)已知方程有一個特解為，試求這方程的通解，并確定。if we dont do that it will go on and go on. we have

4、 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 wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says the matter has been exaggerated

5、 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. 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 spi

6、rit 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 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

7、 there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations 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 t

8、old 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 against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has als

9、o ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic descent could happ

10、en 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 no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmospher

11、e (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 the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (cal

12、led 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 step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool that he wants t

13、o 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 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

14、) - 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 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

15、 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 if he loses consciousn