电大常微分方程复习题小抄参考

1、 一、常微分方程期末考试范围：第一章第五节奇解与包络不考第二章第三节机械振动与rlc回路不考第四节一般线性微分方程的一些解法不考第三章第三节常系数非齐次线性方程组的解法不考二、考试题型填空题（24分）、选择题（20分）、证明题（6分）、计算题（50分）三、各章分数大体分布情况第一章 约40分第二章 约35分第三章 约25分 常微分方程期末复习试题 一 填空题 1、当_时，方程m(x,y)dx+n(x,y)dy=0称为恰当方程，或称全 微分方程。2、_称为齐次方程。3、若为n阶齐线性方程的n个解，则它们线性无关的充要条件是_。4、方程组的_称之为的一个基本解组。5、 称为一阶线性方程，它有积分因

2、子 ，其通解为 。6、若和都是的基解矩阵，则和具有的关系： 。二、计算题1、求解方程：=2、解方程： (2x+2y-1)dx+(x+y-2)dy=03、求解常系数线性方程：4、试求方程组的一个基解矩阵，并计算5、 6、 7、 8、 9、 10、 常微分方程期末考试试卷(6)参考答案一、 填空题1、2、3、w4、n个线性无关解向量5、形如的方程，6、 （c为非奇异方程）二、计算题1、解： (x-y+1)dx-(x+3)dy=0 xdx-(ydx+xdy)+dx-dy-3dy=0 即d-d(xy)+dx-3dy=0 所以2、解：，令z=x+y则所以 z+3ln|z+1|=x+， ln=x+z+即3

3、、解： (1) 齐次方程的通解为x= (2)不是特征根，故取代入方程比较系数得a=，b=-于是 通解为x=+4、解： det()= 所以， 设对应的特征向量为 由 取 所以，= 5、解：故方程的通解为6、解：两边除以： 变量分离： 两边积分：即： 7、解：积分：故通解为：8、解：齐线性方程的特征方程为，故通解为不是特征根，所以方程有形如把代回原方程 于是原方程通解为9、解：齐线性方程的特征方程为，解得于是齐线性方程通解为令为原方程的解，则得，积分得； 故通解为10、解： 则 从而方程可化为 ， 积分得 if we dont do that it will go on and go on. we

4、 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 the matter has been exagge

5、rated 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 because it is against th

6、e 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 football.the (lack of) a

7、ir 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 asked to meet yaya toure,

8、 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 footballs governing body, ha

9、s 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 supersonic descent could

10、 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 the lower level of the atmo

11、sphere (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 crosses the boundary layer

12、 (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 swimming pool that he wa

13、nts 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 of sound - 690 mph (1,11

14、0 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 that can be deployed to slo

15、w 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 conscious