電大常微分方程第二版答案第6章61小抄參考

1、專業(yè)好文檔習(xí) 題 6-11 求出齊次線性微分方程組 的通解，其中a（t）分別為：（1） ；（2） ；（3）。（1）方程組的分量形式為： ，從后一式容易求出的通解為 ，其中k為任意常數(shù)，可分別取和 ，代入前一式得到兩個(gè)相應(yīng)的特解，和 這樣就求得方程組的一個(gè)解矩陣為 又 。因此，是方程組的一個(gè)基解矩陣，根據(jù)定理6.1 ,方程的通解為 （2）方程的分量形式為 由、可和 由觀察法知，為此方程的兩個(gè)特解，將其代入式可得兩個(gè)相應(yīng)的特解，將其代入式可得兩個(gè)相應(yīng)的特解：，。這樣就求得方程組的一個(gè)解矩陣為 又 ，因此中方程組的一個(gè)基解矩陣。故方程組的通解為（3）程組的分量形式為：解 +得 解 -得 解之得 由、

2、可得 又由得 由此可求得方程組的一個(gè)解矩陣 顯然，因此是方程組的一個(gè)基解矩陣，故方程組的通解為3試證向量函數(shù)組 ， ， 在任意區(qū)間 上線性相關(guān)，則存在不全為零的三個(gè)常數(shù) 使得即 而式之左端是一個(gè)不高于二次的多項(xiàng)式，它最多只可能有二個(gè)零點(diǎn)，同此這與式在上恒等于零矛盾，從而得證。4試證基解矩陣完全決定齊次線性方程組即如果方程組 與有一個(gè)相同的基解矩陣，則 證：設(shè)這兩個(gè)方程組的相同基解矩陣為 那么，必有 ,故可逆,設(shè)逆矩陣為,同而 證畢6設(shè)當(dāng)時(shí)，非齊次線性方程組 （1）中的不恒為零。證明（1）有且至多有 n+1個(gè)線性無關(guān)解。證 設(shè)是方程組（1）的相應(yīng)齊次方程組的n個(gè)線性無關(guān)的解，是（1）任意一個(gè)特解

3、，則 是(1)的n+1個(gè)線性無關(guān)解.這是因?yàn)?若存在常數(shù) 使得則一定有 否則有 這與為(1)的解矛盾，因此， 假設(shè)可知故，所以（1）n+1個(gè)線性無關(guān)的解。又設(shè) 是（1）在(a,b)上的任一解，是（1）的n+1個(gè)線性無關(guān)的解， 那么， 是(1)的對(duì)應(yīng)齊次方程組 （2）的解，而（2）最多有n個(gè)線性無關(guān)的解，所以必存在不全為零的常數(shù) 使得 即 顯然，否則，存在不全為零的常數(shù) 使得 這與線性無關(guān)矛盾，故 這說明（1）的任一解，都可由這n+1個(gè)線性無關(guān)的解的線性表出，同時(shí)也說明（1）的任意n+2個(gè)解線性相關(guān)，故方程組（1）在（a，b）上至多有n+1個(gè)線性無關(guān)解。if we dont do that it

4、 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 wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says t

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

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

7、 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 and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have

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

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

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

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

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

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

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

15、at 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 at ma