问题 填空题

设y1=ex,y2=ex+e2x,y3=ex+e-x是二阶常系数非齐次微分方程y’’+Py’+qy=f(x)的三个特解,则该方程为______.

答案

参考答案:y’’-y’-2y=-2ex

解析: 由题设可知,y2-y1=e2x,y3-y1=e-x为对应齐次方程的解,所以对应方程的特征根为λ1=2,λ2=-1,特征方程为(λ-2)(λ+1)=0,即λ2-λ-2=0,所以对应齐次方程为y’’-y’-2y=0,于是原方程为y’’-y’-2y=f(x),将y1=ex代入方程可得f(x)=-2ex
故该方程为y’’-y’-2y=-2ex

阅读理解

     A young man from a village called Nawalapitiya married a young woman from Maliyuwa, a nearby

village. They lived with the man's big family-his parents, his brothers, their wives and children. The family

kept an elephant, in which the young woman soon took a great interest. Every day she fed it with fruit

and sugar.

     Three months later the woman went back to her parents' home, having quarrelled with her husband.

Soon the elephant refused to eat and work. It appeared to be ill and heart-broken. One morning after

several weeks the animal disappeared from the house.

     It went to the woman's home. On seeing her, the elephant waved its trunk and touched her with it.

The young woman was so moved (感动) by the act of the animal that she returned to her husband's home.

1. The writer wrote the story in order to _______.

A. show that elephants are very clever

B. tell how a woman trained a wild animal

C. show that women care more for animals than men do

D. tell how an animal reunited a husband and wife

2. The woman left her new home _______.

A. to visit her own parents in Maliyuwa

B. to see if the elephant would follow her

C. because she was angry with her husband

D. because she was tired of the large family

3. After the young woman left her husband's home, the elephant _______.

A. returned to the forest

B. was sad because it missed her

C. went to look for a new home

D. was sick because nobody fed it

4. The young wife went back to her husband because _______.

A. she knew he had sent the animal to her

B. the elephant had come to look for her

C. her parents persuaded her to

D. she missed her new home

判断题