11-12-2重修复习资料

I.Vocabulary and Structure.

1.I didn’t answer the phone ____D____ I didn’t hear it ring.

A. if

B. unless

C. although

D. because

2.In his report of the accident he ___A_____ some important details.

A. missed

B. wasted

C. escaped

D. failed

3._____C___ a wonderful trip he had when he traveled in China!

A. Where

B. How

C. What

D. That

4.We’re going to __B______ the task that we haven’t finished.

A. take away

B. carry on

C. get onto

D. keep off

5.Sh e didn’t receive the application form; it __C____ to the w

6.rong address.

A. sent

B. be sent

C. was sent

D. being sent

7.She gave up her __A______ as a reporter at the age of 25.

A. career

B. interest

C. life

D. habit

8.It is necessary to find an engineer ___D_____ has skills that meet your needs.

A. whom

B. which

C. whose

D. who

9.Time __B______ very fast and a new year will begin soon.

A. takes off

B. goes by

C. pulls up

D. gets along

10.T his new style of sports shoes is very popular and it is ___C_____ in all sizes.

A. important

B. active

C. available

D. famous

11.T he general manager sat there, ___D_____ to the report from each department.

A. to listen

B. listen

C. being listened

D. listening

12.A fter the robbery, the shop installed a sophisticated alarm system as an insurance ____C____ further losse s.

A. for

B. from

C. towards

D. against

13.A healthy life is frequently thought to be ______D__ with the open countryside and homegrown food.

A. associated

B. tied

C. bound

D. involved

14.F eatures such as height, weight, and skin color ____B____ from individual to individual and from face to face.

A. change

B. vary

C. alter

D. convert

15.____A____ might be expected, the response to the question was very mixed.

A. As

B. That

C. It

D. What

16.H e gives people the impression ___A_____ all his life abroad.

A. of having spent

B. to have spent

C. of being spent

D. to spend

17.J ohn Dewey believed that education should be a preparation for life, that a person learns by doing, and that teaching must ___B_____ the curiosity and creativity of childre n.

A. seek

B. shape

C. stimulate

D. secure

18.T here was a heavy fog this morning, so none of the planes could ______B__.

A. get through

B. take off

C. pull out

D. break away

19.I remember ____B____ to help us if we ever got into trouble.

A. once offering

B. to offer him

C. him to offer

D. him once offering

20.T he crop has similar qualities to the previous one, ____C____ both wind resistant and adapted to the same type of soi l.

A. been

B. to be

C. being

D. having been

21.I am looking forward to C from you as soon as possible.

A. hear

B. be hearing

C. hearing

D. have heard

22.I am looking forward to C from you as soon as possible.

A. hear

B. be hearing

C. hearing

D. have heard

23.H e A that the people he works with are all very interested in their job.

A. feels

B. tries

C. looks

D. asks

24. D , a friend of Mrs. Black found the watch she had lost two days before.

A. Especially

B. Usually

C. Generally

D. Fortunately

25.F ew people B applied for the position meet the requirements of the company.

A. whom

B. who

C. what

D. whose

26.W hy didn’t you A that pencil which was on the floor?

A. pick up

B. bring up

C. get up

D. put up

27.M ary found A extremely difficult to pass the examination.

A. it

B. this

C. that

D. what

28.S he tried hard, but she still couldn’t make us our mind.

A. to change

B. changed

C. change

D. changing

29.F ew people B applied for the position meet the requirements of the company.

A. whom

B. who

C. what

D. whose

30.W hy didn’t you A that pencil which was on the floor?

A. pick up

B. bring up

C. get up

D. put up

31.M ary found A extremely difficult to pass the examination.

A. it

B. this

C. that

D. what

32.S he tried hard, but she still c ouldn’t make us our mind.

A. to c hange

B. changed

C. change

D. changing

33.I w as late for the interview because the bus on the way to London.

A. got off

B. brought in

C. kept off

D. broke down

34.T he manager required that all the employees B at the office before 9:00 in the

morning.

A. will arrive

B. arrive

C. arrived

D. have arrived

35.S he was talking about her C as a nurse in a hospital, which we had never heard of.

A. expenses

B. excuses

C. experiences

D. expressions

36.M y impression of the service in the hotel was that it had really A.

A. improved

B. implied

C. imported

D. imagined

37.p oliceman stopped the driver and found that he B alcohol.

A. drinks

B. has drunk

C. is drinking

D. had drunk The

38.T here are three colors in the British flag, B red, white and blue.

A. rarely

B. namely

C. really

D. naturally

39.I can’t find the key to my office. I C have lost it on my way home.

A. would

B. should

C. must

D. ought to

40.D avid has B much work to do that he is staying late at his office.

A. such

B. so

C. very

D. enough

41.I tried hard, but I couldn’t find the A to the problem.

A. solution

B. help

C. reply

D. demand

42. D writing a letter to the manager, he decided to talk to him in person.

A. Due to

B. Because of

C. As for

D. Instead of

43.A s far as I’m concerned, I don’t like A in that way.

A. to be treated

B. to treat

C. treated

D. treating

44.L isa was busy taking notes C Mark was searching the Internet for the information.

A. until

B. unless

C. while

D. if

45.T here was a heavy fog this morning, so none of the planes could B .

A. get through

B. take off

C. pull out

D. break away

46.I can’t _____C___ my feelings in words.

A. consult

B. imply

C. convey

D. infer

47.F loods cause billions of dollars worth of property damager ____C____.

A. relatively

B. actually

C. annually

D. comparatively

48.T he stock market crash ________ many people.

A. destroyed

B. ruined

C. damaged

D. injured

49.U pon seeing what had happened I could no longer _____C___ myself.

A. hold

B. control

C. manage

D. subdue

50.S he ____D____ her face in 20 minutes in the morning.

A. made out

B. made for

C. made up to

D. made up

51.I have a ___A_____ conscience about forgetting to post your letter.

A. guilty

B. guilt

C. innocent

D. innocence

52.S ince 1970, millions of enthusiasts ___B_____ a substance—vitamin C, which they believe can cure the common cold.

A. have taken

B. have been taking

C. have been taken

D. have being taken

53.The secretary ________ a list of their products to the letter when she posted it.

A. attached

B. fastened

C. secured

D. tied

54.T he mayors from all major cities were called on to deal with some economic ______C__.

A. questions

B. issues

C. pressure

D. stress

55.S ome students like _____C___ a room with others while some prefer being alone.

A. parting

B. sleeping

C. living

D. sharing SECTION B:

56.T he only hope I (have) was that we might reach the port before dark.

57.(publish) in a large press, his novel attracted much attention.

58.S he is growing up now. Y ou shouldn’t speak to her as if she (be) a child.

59.T he practical approach of (take) things professionally will save your time.

60.A s we have reached the decision, no (far) discussion is necessary.

61.T here is a large amount of fossil fuel on earth, but the sun supplies an (limit)

supply of energy.

62.T he residents in this city are always smiling, ________ (energy), well-dressed, farsighted and

broadminded.

63.T he policemen ________ (tell) not to take any action until they received further notice.

64.S omething we want but may not be able to get is ________ (valuable) than something we

have or can easily get.

65.A s soon as I saw it I decided I was going to spend the rest of my life ________ (study) the

animal.

66.S ome new buildings ________ (build) up on the new campus since we entered the university.

67.H e asked whether he was to lock the car or leave it ________ (unlock).

68.T he man was standing by the door with his arms ________ (fold).

69.A lthough she was totally ________ (experienced), she was chosen over more than a thousand

other actresses for a role in “Superwoman”.

70.T he police, ________ (concentrate) most of their efforts on other kinds of crimes, are unable

to take good care of the streets.

71.H e managed ________ (find) the telephone number I had given him before.

72.T he school is located on the side of the mountain, (peace) and quiet.

73.W hen the little girl went upstairs, she felt that something (climb) over her leg.

74.D uring our chat, customers began coming in and sitting down (comfort) at nearby

tables.

75.W e are expected (complete) the whole system by early 2008 at a cost of about $ 2

million.

76.I t is a great honor for me (invite) to speak to you this evening.

77.T he students, (surprise) at the way the questions were put, didn’t know the

answers to them.

78.T he purpose of insurance is (provide) protection against financial loss at a

reasonable cost.

79.I need some (advise) and opinions from Mr. Richard, who has much experience

in engineering designing.

80.T he rocket was about (launch) when an error was found with its control part.

81.D on’t pursue two aims at once or you (gain) neither.

82.T he young often hope to gain (recognize) through individual efforts.

83.T he old lady couldn’t do anything except (complain) about something.

84.L ooking through the window at all the cars on the road, John saw that the traffic was much

________ (heavy) than it had been an hour ago.

85.T hey (sell) three hundred of the cars since the beginning of the year.

II.Reading Comprehension.

People in some countries cannot use their native language for Web addresses. Neither can Chinese speakers, who have to rely on pinyin. But last Friday, ICANN, the Web’s governing body, approved the use of up to 16 languages for the new system. More will follow in the coming years.

The Internet is about to start using the 16 languages of the world. People will soon be able to use addresses in characters (字符) other than those of the Roman alphabet (字母表). The change will also allow the suffix (后缀) to be expressed in 16 other alphabets, including traditional and simplified Chinese characters.

But there are still some problems to work out. Experts have discussed what to do with characters that have several different meanings. This is particularly true of Chinese.

Most experts doubt the change will have a major effect on how the Internet is used. “There will be some competition betwee n companies to obtain popular words for addresses.”

86.F or Web addresses, Chinese speakers now have to use ________.

A. pinyin

B. signs

C. numbers

D. characters

87.T he approval of the use of 16 languages by ICANN will allow web users to ________.

A. change their email address

B. email their messages in characters

C. have the chance to learn other languages

D. use addresses in their own language

88.T he new system will allow the suffix of a Web address to be expressed by ________.

A. any native language

B. figures and numbers

C. Chinese characters

D. symbols and signs

89.W hich of the following is one of the problems in using the new system?

A. Certain characters have several different meanings.

B. Chinese is a truly difficult language to learn.

C. People find it difficult to type their address in characters.

D. Some experts think it is impossible to use Chinese characters.

90.M any experts do not believe that ________.

A. there are still some problems to work out

B. there will be competition to get popular addresses

C. companies are willing to change their web addresses

D. the change will affect the use of the Internet greatly

It is often difficult for a man to be quite sure what tax he ought to pay to the government because it depends on so many different things: whether the man is married; how many children he has; whether he supports any relations; how much he earns; how much interest he receives; how much he has spent on his house during the year, and so on and so forth. All this makes it difficult to decide exactly how much the tax is.

There was a certain artist who was always very careful to pay the proper amount.

One year, after posting his check as usual, he began to wonder if he had paid enough, and after a lot of work, with a pencil and paper, decided that he had not. He believed that he owed the government something.

He was just writing another check to send to the tax-collector when the postman dropped a letter into the box at the front door. Opening it, the artist was surprised to find inside it a check for five pounds from the tax-collector. The official explained that too much had been paid, and that therefore the difference was now returned to the taxpayer.

91.A ccording to the passage, to decide the exact amount of tax to be paid is ___________.

A. simple

B. easy

C. difficult

D. interesting

92.I t is mentioned in the passage that one has to pay tax according to __________.

A. how much education one has received.

B. whether one is single or married

C. how old one’s children are

D. where one lives

93.T he word “proper” in the first line of the second paragraph means__________.

A. small

B. big

C. right

D. wrong

94.A fter a lot of work, the artist thought that he had paid the government___________.

A. less tax than he should have

B. more tax than he should have

C. as much tax as usual

D. just enough tax

95.W hy did the tax-collector send a letter to the artist?

A. To send him a new tax form.

B. To return the money overpaid

C. To remind him of paying the tax

D. To explain the rules of taxpaying

Almost every family buys at least one copy of a newspaper every day. Some people subscribe (订阅) to as many as two or three newspapers. But why do people read newspapers? Five hundred years ago, news of important happenings —— battles lost and won, kings or rulers overthrown (推翻) or killed ——took months and even years to travel from one country to another. The news passed by word of mouth and was never accurate. Today we can read in our newspapers of important events that occur in far away countries on the same y they happen.

Apart from supplying news from all over the world, newspapers give us a lot of other useful information. There are weather reports, radio, television and film guides, book reviews, stories and, of course, advertisements. The bigger ones are put in by large companies to bring attention to their products. They pay the newspapers thousands of dollars for the advertising space, but it is worth the money, for news of their products goes into almost every home in the country. For those who produce newspapers, advertisements are also very important. Money earned from advertisements makes it possible for them to sell their newspapers at a low price and still make a profit.

Newspapers often have information on gardening, cooking and fashion as well as a small but very popular section on jokes and cartoons(漫画)

96.T he habit of reading newspapers is ________.

A. uncommon in the world

B. not popular in U. S. A.

C. widespread in the world

D. founded among a few families

97.A few hundred years ago news did not ________.

A. receive attention

B. travel fast

C. spread to other countries

D. take long to reach other countries

98.I n the past, news was ________.

A. sent by telegraph

B. passed from one person to another

C. sent by letter

D. sent by telephone

99.T he money spent on advertisements is ________.

A. wasted

B. not much

C. worthwhile

D. useless

100.The section on jokes and cartoons is ________.

A. read only by children

B. of no value

C. not helpful

D. read by many

As he closed his service station at 1:20 one Sunday morning, Tony Payseur set on the ground a metal cash box containing $7000.

At home a short while later, he reached in the back of his car for the box. It was missing.

Realizing that he must have left it outside the station, Payseur speeded back.. The box was gone. Sunday morning, although he felt ill, Payseur went to work with his two sons. Then, in the middle of the afternoon, a man named Wayne came and told his story. Passing the station minutes after Payseur left the previous night, Brazzel had spotted the metal box. Thinking it was a tool-box someone had left accidentally, he stopped and picked it up. About 3 p.m. Sunday, Brazzell opened the box. Finding it filled with cash, he rushed to the station.

“I couldn’t believe someone would be so honest,” Payseur said it when he got back his box. 101.What is the passage mainly about?

A. How the missing metal box was returned.

B. Mr. Payseur is a lucky man.

C. Mr. Payseur’s metal box.

D. Mr. Payseur’s carelessness.

102.When did Mr. Payseur realized the missing of his metal box?

A. Saturday morning.

B. Sunday afternoon.

C. A little time after he got home.

D. A little time before he went home.

103.Mr. Wayne found the metal box ________.

A. on the ground with the cover open.

B. laid on the ground

C. lying in the corner

D. in the back of a car

104.Brazzell had spotte d the metal box. (para.2) Here “spot” means ________.

A. catch

B. meet

C. know

D. see

105.By saying “I couldn’t believe someone would be so honest.” Mr. Payseur means that ________.

A. it’s hard to believe he is so honest

B. there are honest people like Mr. Payseur

C. we should believe most of the people

D. Mr. Brazzell is a nice man

Online advertising is the means of selling a product on the Internet．With the arrival of the Internet，the business world has become digitalized(数字化)and people prefer buying things online，which is easier and faster．Online advertising is also known as e-advertising．It offers a great variety of services，which can not be offered by any other way of advertising．One major benefit of online advertising is the immediate spread of information that is not limited by geography or time．Online advertising can be viewed day and night throughout the world. Besides, it reduces the cost and increases the profit of the company．

Small businesses especially find online advertising cheap and effective．They can focus on their ideal customers and pay very little for the advertisements．

In a word，online advertising is a cheap and effective way of advertising，whose success has so far fully proved its great potential(潜力)．

106.According to the first paragraph，buying things online is more ____ ．

A. convenient

B. fashionable

C. traditional

D. reliable

https://www.sodocs.net/doc/045780221.html,pared with any other way of advertising，online advertising ____ ．

A. attracts more customers

B. displays more samples

C. offers more services

D. makes more profits

108.Which of the following statements is TRUE of online advertising?

A. It has taken the place of traditional advertising．

B. It will make the Internet technology more efficient．

C. It can help sell the latest models of digitalized products．

D. It can spread information without being limited by time．

109.Who can especially benefit from online advertising?

A. Local companies.

B. Small businesses.

C. Government departments.

D. International organization.

110.This passage is mainly about ____ ．

A. the function and the use of the Internet

B. the application of digital technology

C. the development of small businesses

D. the advantages of online advertising

III.Translation.

SECTION A:

111.People with a naturally happy disposition are sunny and pleasant to be around.

112.Maybe extreme-sport people are merely striking a blow for truly unique experiences. 113.While colleges are allocating a greater share of financial aid to student loans, tuition increases are outpacing inflation.

114.The opposite belief, that money brings misery is just as false, for one could as easily find examples of wealthy people who are perfectly content with life.

115.In the 1920s advertisers and their agents had come to realize the radio’s possibilities. 116.In the same way, the genuine laughter that comes from true happiness is infectious and brings happiness to all.

117.Along with their return, they also brought back an appetite for the pizza they had eaten and enjoyed in Italy.

118.The more we are driven by such forces as greed and desire, the more likely it is we will lose our stock of happiness.

119.These firms began to market their packaged goods under brand names.

120.There’s nothing wrong with trying new lifestyles, but students may forget just how expensive this can be if they begin doing it several times a week.

SECTION B:

121.安妮尽一切可能使婚姻不致破裂。

122.就人口而言，华盛顿还不能算是一个大城市。

123.20世纪初，两位美国人从飞鸟那里获得灵感，发明了飞机。

124.那位演员在成名前，经历了一段艰难困苦时期。

125.考虑到公司的财务状况，经理认为每个人的费用不应超过100美元。

126.这种疾病常以发高烧的形式出现。

127.现代科技已将人们从繁重的家务中解放出来。

128.学生们逐渐认识到，需要多年的时间才能掌握一门外语。

129.在管理中，评价员工的工作是很难的。

130.这篇文章里有一些我们难以理解的句子。

131.汤姆不想因学费增加父母的负担。

132.该公司在这场金融危机中蒙受了巨大损失。

常微分方程期末考试练习题及答案

一，常微分方程的基本概念 常微分方程： 含一个自变量x，未知数y及若干阶导数的方程式。一般形式为：F（x，y，y，.....y(n)）=0 (n≠0). 1. 常微分方程中包含未知函数最高阶导数的阶数称为该方程的阶。如：f(x)（3）+3f(x)+x=f(x)为3阶方程。 2.若f（x）使常微分方程两端恒等，则f（x）称为常微分方程的解。 3.含有独立的任意个常数（个数等于方程的阶数）的方程的解称为常微分方程的通解。如常系数三阶微分方程F（t，x（3））=0的通解的形式为：x（t）=c1x（t）+c2x（t）+c3x（t）。 4.满足初值条件的解称为它的特解（特解不唯一，亦可能不存在）。 5.常微分方程之线性及非线性：对于F（x，y，y，......y(n)）=0而言，如果方程之左端是y，y，......y(n)的一次有理式，则次方程为n阶线性微分方程。（方程线性与否与自变量无关）。如：xy（2）-5y，+3xy=sinx 为2阶线性微分方程；y（2）+siny=0为非线性微分方程。 注：a.这里主要介绍几个主要的，常用的常微分方程的基本概念。余者如常微分方程之显隐式解，初值条件，初值问题等概念这里予以略去。另外，有兴趣的同学不妨看一下教材23页的雅可比矩阵。 b.教材28页第八题不妨做做。 二.可分离变量的方程 A.变量分离方程

1.定义：形如 dx dy =f （x)φ(y)的方程，称为分离变量方程。这里f （x ），φ（x ）分别是x ，y 的连续函数。 2.解法：分离变量法? ? +=c dx x f y dy )()(?. （*） 说明： a 由于（*）是建立在φ（y ）≠0的基础上，故而可能漏解。需视情况补上φ（y ）=0的特解。（有时候特解也可以和通解统一于一式中） b.不需考虑因自变量引起的分母为零的情况。 例1.0)4(2=-+dy x x ydx 解：由题意分离变量得：04 2=+-y dy x dx 即： 0)141(41=+--y dy dx x x 积分之，得：c y x x =+--ln )ln 4(ln 4 1 故原方程通解为：cx y x =-4)4( （c 为任意常数），特 解y=0包含在通解中（即两者统一于一式中）。 *例2.若连续函数f （x ）满足 2 ln )2 ()(20 +=? dt t f x f x ，则f （x ）是？ 解：对给定的积分方程两边关于x 求导，得： )(2)('x f x f = （变上限求积分求导） 分离变量，解之得：x Ce x f 2)(= 由原方程知： f （0）=ln2， 代入上解析式得： C=ln2， B.可化为分离变量方程的类型。 解决数学题目有一个显而易见的思想：即把遇到的新问题，结合已知

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常微分方程期末考试试卷 学院 ______ 班级 _______ 学号 _______ 姓名 _______ 成绩 _______ 一． 填空题 （30分） 1．)()(x Q y x P dx dy += 称为一阶线性方程，它有积分因子 ? -dx x P e )( ，其通解为 _________ 。 2．函数),(y x f 称为在矩形域R 上关于y 满足利普希兹条件，如果 _______ 。 3． 若)(x ?为毕卡逼近序列{})(x n ?的极限，则有)()(x x n ??-≤ ______ 。 4．方程22y x dx dy +=定义在矩形域22,22:≤≤-≤≤-y x R 上，则经过点（0，0）的解的存在区间是 _______ 。 5．函数组t t t e e e 2,,-的伏朗斯基行列式为 _______ 。 6．若),,2,1)((n i t x i =为齐线性方程的一个基本解组，)(t x - 为非齐线性方 程的一个特解，则非齐线性方程的所有解可表为 ________ 。 7．若)(t Φ是x t A x )('=的基解矩阵，则向量函数)(t ?= _______是 )()('t f x t A x +=的满足初始条件0)(0=t ?的解；向量函数)(t ?= _____ 是)()('t f x t A x +=的满足初始条件η?=)(0t 的解。 8．若矩阵A 具有n 个线性无关的特征向量n v v v ,,,21 ，它们对应的特征值分别为n λλλ ,,21，那么矩阵)(t Φ= ______ 是常系数线性方程组 Ax x ='的一个基解矩阵。 9．满足 _______ 的点),(**y x ，称为驻定方程组。

常微分方程期中考试试卷(2015)

13级常微分方程期中考试试卷 班级__________姓名__________学号________得分__________ 一、填空题（102?'） 1、微分方程0)( 22=+-+x y dx dy dx dy n 的阶数是________________________。 2、微分方程x dx dy 2=与直线32+=x y 相切的解是_____________________。 3、x e y dx dy +=的通解为___________________________________________。 4、若),(y x M 和),(y x N 在矩形区域R 内是),(y x 的连续函数，且有连续的一阶偏导数，则方程0),(),(=+dy y x N dx y x M 有只与y 有关的积分因子的充要条件是__________________________________________。 5、对于任意的),(1y x ，R y x ∈),(2（R 为某一矩形区域），若存在常数 )0(>N N 使_________________， 则称),(y x f 在R 上关于y 满足利普希兹条件。 6、如果),(y x f 在有界区域G 中连续，在G 内满足利普希兹条件，则方程),(y x f dx dy =的通过G 内任一点),(00y x 的解)(x y ?=可以向左右延拓，直到__________________________________________。 7、方程3 1-++-=y x y x dx dy 经过代换__________________后，可化为齐次方程。 8、若),(y x f 在矩形区域R 上___________________且________________则方程),(y x f dx dy =存在唯一解。 9、微分方程dy dx dx dy x y +=的奇解为_______________________________。 10、若函数组),,2,1)((n i t x i =在],[b a 上线性相关，则=)(t w ___________。

常微分期末考试试题和答案1

《 常微分方程 》期末考试试卷（1） 班级 学号 姓名 成绩 一、填空（每格3分，共30分） 1、方程(,)(,)M x y d x N x y d y +=有只与x 有关的积分因子的充要条件 是 。 2、若12(),(),,()n x t x t x t 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 。 3、若()t Φ和()t ψ都是' ()x A t x =的基解矩阵，则()t Φ和()t ψ具有的关系是 _____________________________。 4、函数),(y x f 称为在矩形域Ｒ上关于y 满足利普希兹条件，如 果 。 5、当 时，方程0),(),(=+dy y x N dx y x M 称为恰当方程， 或称全微分方程。 6、若()t Φ是x t A x )(='的基解矩阵，则x t A x )(=')(t f =满足η=)(0t x 的解 。 7、若()(1,2,,)i x t i n = 为n 阶齐线性方程()() 1()()0n n n x a t x a t x +++= 的n 个线性无关解， 则这一齐线性方程的通解可表为 。 8、求 dx dy =f(x,y)满足00()y x y =的解等价于求积分方程 的解。 9、如果),(y x f 在R 上 且关于y 满足李普希兹条件，则方程 ),(y x f dx dy =存在唯一 的解)(x y ?=，定义于区间h x x ≤-0上 ，连续且满足初始条件00)(y x =?，其中 h = ，),(max ),(y x f M R y x ∈=。

二、计算题(每题10分,共50分) 10、求方程 22 1dy y dx xy x y += + 的解。 11、求方程 2 dy x y dx =-通过点(1,0)的第二次近似解。 12、求非齐线性方程sin x x t ''+=的特解。 13、求解恰当方程 0)4()3(2=---dy x y dx x y 。 14、求伯努利方程 的通解。2 6 xy x y dx dy -= 三、证明.（20分） 15、1)试验证初值问题2 11 4x x ??'=? ?-??，12(0)η?ηη?? ==???? 的解为: 1123212()()()t t t e t ηηη?ηηη+-+?? =??+-+?? ; 2）求该微分方程组的expAt 。 试卷（1）答案 一、填空（每格3分，共30分） 1、方程(,)(,)0M x y dx N x y dy +=有只与x 有关的积分因子的充要条件 是 )(x N x N y M ?=??-??。 2、若12(),(),,()n x t x t x t 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12[(),(),,()]0n w x t x t x t ≠ 。