電大常微分方程課程作業(yè)4解答

1、專業(yè)好文檔常微分方程課程作業(yè)4解答1. 解答：證：首先，方程的任意兩個(gè)線性無關(guān)解的郎斯基行列式在區(qū)間i上恒不為零?？杀砣缦?，為區(qū)間i上任一點(diǎn)。由于， 在區(qū)間i上連續(xù)、恒不為零。故在區(qū)間i上恒不為零，即同號(hào)。此即 （與同號(hào)）在區(qū)間i上不變號(hào)。亦即在區(qū)間i上嚴(yán)格單調(diào)。2. 解答：證：設(shè)二階線性齊次方程的任意兩個(gè)線性無關(guān)解組的郎斯基行列式分別為： a , b分別為這兩個(gè)行列式在某一點(diǎn)的值。由于線性無關(guān)解組的行列式恒不為零。故a , b都不為零。兩個(gè)行列式之比或?yàn)榉橇愠?shù)。3. 解答：方程可變?yōu)?通解為：以 代入得 = = = =4. 解答： 或 顯然 當(dāng)為常數(shù)時(shí)，（比如 =0就能如此）其基本解組的

2、郎斯基行列式為常數(shù)。5. 解答： （1） 方程的特征方程為 特征根為 所以方程的通解為 ，其中為任意常數(shù)。（2） 方程的特征方程為 特征根為 所以方程的通解為 ，其中，為任意常數(shù)。（3） 方程的特征方程為 特征根為 所以方程的通解為 ，其中，為任意常數(shù)。6. 解答：（1） 方程的特征方程為 特征根為 所以方程的通解為 ，其中為任意常數(shù)。以代入下兩式， 得 所以 方程滿足初始條件的解為 （2） 方程的特征方程為 特征根為 所以方程的通解為 ，其中為任意常數(shù)。以代入下兩式 得 所以 方程滿足初始條件的解為 7. 解答：（1）齊次方程的特征方程為特征根為 通解為 ，其中為任意常數(shù)。令 代入比較同次項(xiàng)

3、系數(shù)得 所以方程的通解為（2）齊次方程的特征方程為特征根為 通解為 ，其中為任意常數(shù)。令 代入比較同次項(xiàng)系數(shù)得 所以方程 的通解為（3）齊次方程的特征方程為特征根為 通解為 ，其中為任意常數(shù)。令 代入比較同次項(xiàng)系數(shù)得 所以方程的通解為8. 解答：由 f=k x 以 f=9.8 , x=1 得 k=9.8又 得 即特征方程為 特征根為 通解為 ，其中為任意常數(shù)。令 ， 則有 所求周期為 9. 解答： 由 得 即 的特征方程為 特征根為 通解為 ，其中為任意常數(shù)。令 代入 得 故 的通解為以 t=0 , x=0 , x/=0 代入下兩式 ， 所以質(zhì)點(diǎn)的運(yùn)動(dòng)規(guī)律為： if we dont do th

4、at 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 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 s

5、ays the 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 spect

6、ators 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 o

7、ut of 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

8、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 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 europea

9、n footballs 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 aborte

10、d.the 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 throu

11、gh the 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

12、 he crosses 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

13、 of a 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

14、speed 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 parachu

15、te 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 consciou