最新2007年7月自考常微分方程试题试卷真题知识点复习考点归纳总结参考.doc

高等教育自学考试常微分方程试题一、填空题(本大题共12小题，每空2分，共28分)请在每小题的空格中填上正确答案。错填、不填均无分。1.方程y+p(x)y=q(x)yn(n0,1)称为_方程,用变换_可化为线性方程.2.函数f(x,y)在平面区域d中满足对y的李普希兹条件的一个充分条件是_.3.设由解的存在唯一性定理,其解的存在区间是_.4.设,且0(x)=1,试用逐次逼近法求第二次近似解2(x)=_.5.方程y=xy+ (y)称为克莱罗方程,如取 (y)=,则其通解为_;奇解为_.6.与初值问题y+2y+7xy=e-x,y(1)=7,y(1)=-2等价的一阶方程组的初值问题为_.7.已知y+p(x)y+q(x)y=0的一特解为y1(x),则其另一个与其线性无关的解可表示为_.8.若a是一个对角形矩阵a=,则exp at=_.9.设(t)、exp at都是方程组=ax的基解矩阵,（a（）是实常数矩阵）,则它们之间成立_.10.n阶线性齐次方程有且仅有_个线性无关解。11.n阶常系数线性齐次方程,若其特征根均有负实部，则当x+时其任何解y=y(x)有性质：_.12.线性系统奇点的类型为_.二、求下列方程的通解(本大题共3小题，每小题9分，共27分)1.(x+1) (x+1)n+1.2.(y-x(x2+y2)dx-xdy=0.3.yy+y2=0.三、求下列方程的通解(本大题共3小题，每小题9分，共27分)1. +4x=cost+e2t.2.y+2ay+a2y=ex.3.四、证明题(本大题9分)试导出并证明方程m(x,y)dx+n(x,y)dy=0具有形如=(x)积分因子的充要条件.五、讨论题(本大题9分)判定系统零解的稳定性.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