电大常微分方程第二版答案第6章61小抄参考

1、专业好文档习 题 6-11 求出齐次线性微分方程组 的通解，其中a（t）分别为：（1） ；（2） ；（3）。（1）方程组的分量形式为： ，从后一式容易求出的通解为 ，其中k为任意常数，可分别取和 ，代入前一式得到两个相应的特解，和 这样就求得方程组的一个解矩阵为 又 。因此，是方程组的一个基解矩阵，根据定理6.1 ,方程的通解为 （2）方程的分量形式为 由、可和 由观察法知，为此方程的两个特解，将其代入式可得两个相应的特解，将其代入式可得两个相应的特解：，。这样就求得方程组的一个解矩阵为 又 ，因此中方程组的一个基解矩阵。故方程组的通解为（3）程组的分量形式为：解 +得 解 -得 解之得 由、

2、可得 又由得 由此可求得方程组的一个解矩阵 显然，因此是方程组的一个基解矩阵，故方程组的通解为3试证向量函数组 ， ， 在任意区间 上线性相关，则存在不全为零的三个常数 使得即 而式之左端是一个不高于二次的多项式，它最多只可能有二个零点，同此这与式在上恒等于零矛盾，从而得证。4试证基解矩阵完全决定齐次线性方程组即如果方程组 与有一个相同的基解矩阵，则 证：设这两个方程组的相同基解矩阵为 那么，必有 ,故可逆,设逆矩阵为,同而 证毕6设当时，非齐次线性方程组 （1）中的不恒为零。证明（1）有且至多有 n+1个线性无关解。证 设是方程组（1）的相应齐次方程组的n个线性无关的解，是（1）任意一个特解

3、，则 是(1)的n+1个线性无关解.这是因为,若存在常数 使得则一定有 否则有 这与为(1)的解矛盾，因此， 假设可知故，所以（1）n+1个线性无关的解。又设 是（1）在(a,b)上的任一解，是（1）的n+1个线性无关的解， 那么， 是(1)的对应齐次方程组 （2）的解，而（2）最多有n个线性无关的解，所以必存在不全为零的常数 使得 即 显然，否则，存在不全为零的常数 使得 这与线性无关矛盾，故 这说明（1）的任一解，都可由这n+1个线性无关的解的线性表出，同时也说明（1）的任意n+2个解线性相关，故方程组（1）在（a，b）上至多有n+1个线性无关解。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