電大常微分方程復習題小抄參考

1、 一、常微分方程期末考試范圍：第一章第五節(jié)奇解與包絡不考第二章第三節(jié)機械振動與rlc回路不考第四節(jié)一般線性微分方程的一些解法不考第三章第三節(jié)常系數非齊次線性方程組的解法不考二、考試題型填空題（24分）、選擇題（20分）、證明題（6分）、計算題（50分）三、各章分數大體分布情況第一章 約40分第二章 約35分第三章 約25分 常微分方程期末復習試題 一 填空題 1、當_時，方程m(x,y)dx+n(x,y)dy=0稱為恰當方程，或稱全 微分方程。2、_稱為齊次方程。3、若為n階齊線性方程的n個解，則它們線性無關的充要條件是_。4、方程組的_稱之為的一個基本解組。5、 稱為一階線性方程，它有積分因

2、子 ，其通解為 。6、若和都是的基解矩陣，則和具有的關系： 。二、計算題1、求解方程：=2、解方程： (2x+2y-1)dx+(x+y-2)dy=03、求解常系數線性方程：4、試求方程組的一個基解矩陣，并計算5、 6、 7、 8、 9、 10、 常微分方程期末考試試卷(6)參考答案一、 填空題1、2、3、w4、n個線性無關解向量5、形如的方程，6、 （c為非奇異方程）二、計算題1、解： (x-y+1)dx-(x+3)dy=0 xdx-(ydx+xdy)+dx-dy-3dy=0 即d-d(xy)+dx-3dy=0 所以2、解：，令z=x+y則所以 z+3ln|z+1|=x+， ln=x+z+即3

3、、解： (1) 齊次方程的通解為x= (2)不是特征根，故取代入方程比較系數得a=，b=-于是 通解為x=+4、解： det()= 所以， 設對應的特征向量為 由 取 所以，= 5、解：故方程的通解為6、解：兩邊除以： 變量分離： 兩邊積分：待添加的隱藏文字內容2即： 7、解：積分：故通解為：8、解：齊線性方程的特征方程為，故通解為不是特征根，所以方程有形如把代回原方程 于是原方程通解為9、解：齊線性方程的特征方程為，解得于是齊線性方程通解為令為原方程的解，則得，積分得； 故通解為10、解： 則 從而方程可化為 ， 積分得 if we dont do that it will go on an

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

5、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. you can always find money from somebody to pay them.it is a nonsense to have matches played without spectators because it is

6、 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 have today in our game. but it is only with harsh sanctions that racism and discrimination can be washed out of football.the

7、(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 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

8、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 against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governi

9、ng 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 side added: we found no racist insults from fans of cska.baumgartner the disappointing news: mission aborted.the supersonic de

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

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

12、ndary 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 step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom of a swimming pool

13、 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 is diving into the shallow end.skydiver preps for the big jumpwhen he jumps, he is expected to reach the speed of sound - 69

14、0 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 enough to stop him completely.if he goes too fast or spins out of control, he has a stabilization parachute that can be depl

15、oyed 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 conscious