2014年电大常微分方程期末试题A小抄参考.doc

专业好文档得分评卷教师 一、填空题（每空2 分，共16分）。1方程满足解的存在唯一性定理条件的区域是2. 方程组的任何一个解的图象是 维空间中的一条积分曲线.3连续是保证方程初值唯一的 条件4方程组的奇点的类型是 5方程的通解是 6变量可分离方程的积分因子是 7二阶线性齐次微分方程的两个解,成为其基本解组的充要条件是 8方程的基本解组是 得分评卷教师 二、选择题（每小题 3 分，共 15分）。9一阶线性微分方程的积分因子是（ ）（a） （b） （c） （d）10微分方程是（ ）（a）可分离变量方程 （b）线性方程 （c）全微分方程 （d）贝努利方程11方程x(y21)dx+y(x21)dy=0的所有常数解是（ ）(a) (b) (c), (d), 12阶线性非齐次微分方程的所有解（ ） （a）构成一个线性空间 （b）构成一个维线性空间 （c）构成一个维线性空间 （d）不能构成一个线性空间13方程（ ）奇解（a）有一个 （b）有无数个 （c）只有两个 （d）无得分评卷教师 三、计算题（每小题8分，共48分）。14求方程的通解15求方程的通解16求方程的通解17求方程的通解18求方程的通解19求方程组的实基本解组得分评卷教师 四、应用题（本小题 11 分，共11分）。20（1）求函数的拉普拉斯变换（2）求初值问题的解得分评卷教师 五、证明题（本小题10分，共10分）。21 证明：对任意及满足条件的，方程的满足条件的解在上存在。常微分方程复习习题集一 求解下列一阶微分方程1234567891011121314151617二 求解下列微分方程组1. 3. 2. 4. 三 求下列微分方程的通解1. 2. 3. 4. 四 叙述“皮卡存在唯一性定理”，并求下列初值问题1. 2. 的第三次近似解。五 对任意的及满足条件的，求方程的满足初值条件的解的最大存在区间。六 考虑微分方程（1）设与是它的任意两个解，试证与的朗斯基行列式恒等于一个常数；（2）设已知方程有一个特解为，试求这方程的通解，并确定。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 - said 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 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 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) 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 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 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 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 mph, 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 higher 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 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 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 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 consciousness at mac