电大常微分方程试卷(自学考)小抄参考

1、专业好文档绝密启动前2011年10月广东高等教育自学考试常微分方程（b）试卷一、选择题（每小题2分共20分）1.方程是 。 （ ）a、可分离变量方程 b、线性方程c、全微分方程 d、伯努利方程2.微分方程的阶数是 （ ）a、1阶 b、2阶 c、3阶 d、4阶3.方程 过点（0,0）有 （ ）a.一个解 b.两个解 c.三个解 d.四个解4.方程过点（0,0）的解为，此解的最大存在区间是（ ）a. b. c. d. 5.线性非齐次方程组 （ ）a不构成线性空间 b.构成一个n维线性空间c. 构成一个n+1维线性空间 d.构成一个无穷维线性空间6.若是线性齐次方程组的基本解矩阵，c为n阶常数方阵，

2、那么是否还是这个方程组的基本解矩阵 （ ）a.一定是 b.一定不是c.只有当c是非奇非异矩阵时，才是这个方程组的基本解矩阵d.只有当c是单位矩阵时，才是这个方程组的基本解矩阵7.向量函数组在区间i上线性相关的 是在区间i上它的伏郞斯基行列式a.充分条件 b.必要条件 c.充分且必要条件 d.充分但不必要8.一阶非齐次方程组的任意两个非零解之和 （ ）a. 不是其对应齐次方程组的解 b. 是原方程组的通解c. 仍是原方程组的解 d.是其对应齐次方程组的解9.方程的任一非零解在x轴的任意有限区间内a.没有零点 b.只有一个零点c.只有有限个零点 d.有无限个零点10.下列方程的解在第一象限内是严格

3、增加的是 （ ）a. b. c. d. 二、填空题（每小题3分，共24分）11.若方程是恰当方程，则它的通解是 。12.连续是方程初值惟一的 条件。13.设二阶常系数线性非齐次方程的一个特解是则p= 。14.已知线性非齐次方程组的基解矩阵为，则 。15.常数a、b满足 条件时，方程的所有解，当时都趋于零。16.若含有几个未知函数的线性齐次方程组，有相同的基本解组，则和满足 。17.若常系数线性方程组有一个解，则满足 。18.与二阶方程等价的一阶方程组为 。三、计算题：（每题6分，共42分）19.求方程 的通解。20.求方程 +1=0 的通解。21.求方程 的通解。22.求隐式方程 的通解。23

4、.设为连续函数，且满足。求。24.求解线性方程 的通解。四、应用题（7分）：25.求具有性质的函数，已知存在。五、证明题（7分）：26.设在上连续，且（常数），试证明，当时，方程的一切解，均有。if we dont do that 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 - sai

5、d he wanted to meet ivory coast international toure to discuss his complaint.cska general director roman babaev says 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

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

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

8、ons 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 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 procee

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

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

11、h, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through 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 hi

12、gher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as 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

13、slowly step out onto something resembling an olympic diving platform.below, the earth becomes the concrete bottom 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

14、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 - 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

15、 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 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 co