電大常微分方程試卷(自學(xué)考)小抄參考

1、絕密啟動(dòng)前2011年10月廣東高等教育自學(xué)考試常微分方程（b）試卷一、選擇題（每小題2分共20分）1.方程是 。 （ ）a、可分離變量方程 b、線性方程c、全微分方程 d、伯努利方程2.微分方程的階數(shù)是 （ ）a、1階 b、2階 c、3階 d、4階3.方程 過點(diǎn)（0,0）有 （ ）a.一個(gè)解 b.兩個(gè)解 c.三個(gè)解 d.四個(gè)解4.方程過點(diǎn)（0,0）的解為，此解的最大存在區(qū)間是（ ）a. b. c. d. 5.線性非齊次方程組 （ ）a不構(gòu)成線性空間 b.構(gòu)成一個(gè)n維線性空間c. 構(gòu)成一個(gè)n+1維線性空間 d.構(gòu)成一個(gè)無窮維線性空間6.若是線性齊次方程組的基本解矩陣，c為n階常數(shù)方陣，那么是否還

2、是這個(gè)方程組的基本解矩陣 （ ）a.一定是 b.一定不是c.只有當(dāng)c是非奇非異矩陣時(shí)，才是這個(gè)方程組的基本解矩陣d.只有當(dāng)c是單位矩陣時(shí)，才是這個(gè)方程組的基本解矩陣7.向量函數(shù)組在區(qū)間i上線性相關(guān)的 是在區(qū)間i上它的伏郞斯基行列式a.充分條件 b.必要條件 c.充分且必要條件 d.充分但不必要8.一階非齊次方程組的任意兩個(gè)非零解之和 （ ）a. 不是其對(duì)應(yīng)齊次方程組的解 b. 是原方程組的通解c. 仍是原方程組的解 d.是其對(duì)應(yīng)齊次方程組的解9.方程的任一非零解在x軸的任意有限區(qū)間內(nèi)a.沒有零點(diǎn) b.只有一個(gè)零點(diǎn)c.只有有限個(gè)零點(diǎn) d.有無限個(gè)零點(diǎn)10.下列方程的解在第一象限內(nèi)是嚴(yán)格增加的是

3、（ ）a. b. c. d. 二、填空題（每小題3分，共24分）11.若方程是恰當(dāng)方程，則它的通解是 。12.連續(xù)是方程初值惟一的 條件。13.設(shè)二階常系數(shù)線性非齊次方程的一個(gè)特解是則p= 。14.已知線性非齊次方程組的基解矩陣為，則 。15.常數(shù)a、b滿足 條件時(shí)，方程的所有解，當(dāng)時(shí)都趨于零。16.若含有幾個(gè)未知函數(shù)的線性齊次方程組，有相同的基本解組，則和滿足 。17.若常系數(shù)線性方程組有一個(gè)解，則滿足 。18.與二階方程等價(jià)的一階方程組為 。三、計(jì)算題：（每題6分，共42分）19.求方程 的通解。20.求方程 +1=0 的通解。21.求方程 的通解。22.求隱式方程 的通解。23.設(shè)為連續(xù)

4、函數(shù)，且滿足。求。24.求解線性方程 的通解。四、應(yīng)用題（7分）：25.求具有性質(zhì)的函數(shù)，已知存在。五、證明題（7分）：26.設(shè)在上連續(xù)，且（常數(shù)），試證明，當(dāng)時(shí)，方程的一切解，均有。if 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

5、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 with fine

6、s. 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 villains w

7、e 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 celebrations a

8、nd 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 proceedings

9、 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 russian

10、 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 mph, wi

11、th 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 higher

12、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 will slowl

13、y 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 be like

14、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 will not

15、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 if he loses con