電大7月自考常微分方程試題試卷真題小抄參考

1、專業(yè)好文檔做試題,沒答案?上自考365,網(wǎng)校名師為你詳細解答!浙江省2007年7月高等教育自學(xué)考試常微分方程試題課程代碼：10002一、填空題(本大題共12小題，每空2分，共28分)請在每小題的空格中填上正確答案。錯填、不填均無分。1.方程y+p(x)y=q(x)yn(n0,1)稱為_方程,用變換_可化為線性方程.2.函數(shù)f(x,y)在平面區(qū)域d中滿足對y的李普希茲條件的一個充分條件是_.3.設(shè)由解的存在唯一性定理,其解的存在區(qū)間是_.4.設(shè),且0(x)=1,試用逐次逼近法求第二次近似解2(x)=_.5.方程y=xy+ (y)稱為克萊羅方程,如取 (y)=,則其通解為_;奇解為_.6.與初值問

2、題y+2y+7xy=e-x,y(1)=7,y(1)=-2等價的一階方程組的初值問題為_.7.已知y+p(x)y+q(x)y=0的一特解為y1(x),則其另一個與其線性無關(guān)的解可表示為_.8.若a是一個對角形矩陣a=,則exp at=_.9.設(shè)(t)、exp at都是方程組=ax的基解矩陣,（a（）是實常數(shù)矩陣）,則它們之間成立_.10.n階線性齊次方程有且僅有_個線性無關(guān)解。11.n階常系數(shù)線性齊次方程,若其特征根均有負實部，則當(dāng)x+時其任何解y=y(x)有性質(zhì)：_.12.線性系統(tǒng)奇點的類型為_.二、求下列方程的通解(本大題共3小題，每小題9分，共27分)1.(x+1) (x+1)n+1.2.

3、(y-x(x2+y2)dx-xdy=0.3.yy+y2=0.三、求下列方程的通解(本大題共3小題，每小題9分，共27分)1. +4x=cost+e2t.2.y+2ay+a2y=ex.3.四、證明題(本大題9分)試導(dǎo)出并證明方程m(x,y)dx+n(x,y)dy=0具有形如=(x)積分因子的充要條件.五、討論題(本大題9分)判定系統(tǒng)零解的穩(wěn)定性.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

4、 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 by the ivorian and the british media.blatter, 77, said: it has been decided

5、 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 spirit of football and against the visiting team. it is all nonsense.we can do

6、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 there watch mcayman islands-based webb, the head of fifas anti-racism taskf

7、orce, 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 told bbc sport.for me its about how he felt and i would like to speak to him

8、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 also ordered an immediate investigation into the referees actions.cska said the

9、y 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 happen as early as sunda.the weather plays an important role in this mission. st

10、arting 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 atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher

11、 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 (called the tropopause),e can expect a lot of turbulence.the balloon will slowly

12、 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 to land on, but not too hard. still, hell be traveling fast, so despite the d

13、istance, 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) - in less than 40 seconds. like hitting the top of the water, he will begi

14、n 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 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 consciousness