电大常微分方程课程作业4解答

1、常微分方程课程作业4解答1. 解答：证：首先，方程的任意两个线性无关解的郎斯基行列式在区间i上恒不为零。可表如下 ，为区间i上任一点。由于， 在区间i上连续、恒不为零。故在区间i上恒不为零，即同号。此即 （与同号）在区间i上不变号。亦即在区间i上严格单调。2. 解答：证：设二阶线性齐次方程的任意两个线性无关解组的郎斯基行列式分别为： a , b分别为这两个行列式在某一点的值。由于线性无关解组的行列式恒不为零。故a , b都不为零。两个行列式之比或为非零常数。3. 解答：方程可变为 通解为：以 代入得 = = = =4. 解答： 或 显然 当为常数时，（比如 =0就能如此）其基本解组的郎斯基行列

2、式为常数。5. 解答： （1） 方程的特征方程为 特征根为 所以方程的通解为 ，其中为任意常数。（2） 方程的特征方程为 特征根为 所以方程的通解为 ，其中，为任意常数。（3） 方程的特征方程为 特征根为 所以方程的通解为 ，其中，为任意常数。6. 解答：（1） 方程的特征方程为 特征根为 所以方程的通解为 ，其中为任意常数。以代入下两式， 得 所以 方程满足初始条件的解为 （2） 方程的特征方程为 特征根为 所以方程的通解为 ，其中为任意常数。以代入下两式 得 所以 方程满足初始条件的解为 7. 解答：（1）齐次方程的特征方程为特征根为 通解为 ，其中为任意常数。令 代入比较同次项系数得 所

3、以方程的通解为（2）齐次方程的特征方程为特征根为 通解为 ，其中为任意常数。令 代入比较同次项系数得 所以方程 的通解为（3）齐次方程的特征方程为特征根为 通解为 ，其中为任意常数。令 代入比较同次项系数得 所以方程的通解为8. 解答：由 f=k x 以 f=9.8 , x=1 得 k=9.8又 得 即特征方程为 特征根为 通解为 ，其中为任意常数。令 ， 则有 所求周期为 9. 解答： 由 得 即 的特征方程为 特征根为 通解为 ，其中为任意常数。令 代入 得 故 的通解为以 t=0 , x=0 , x/=0 代入下两式 ， 所以质点的运动规律为： 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 consciou