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(math150)[2006](s)final~PPSpider^_10464.pdf
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HKUST
MATH150 Introduction to Di.erential Equations
Final Examination (Version A) Name:
25th May 2006 Student I.D.:
8:30amC10:30am Tutorial Section:

Directions:
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Write your name, ID number, and tutorial section in the space provided above.

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DO NOT open the exam until instructed to do so.

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When instructed to open the exam, check that you have, in addition to this cover page, 8 pages of questions, printed on both sides of each page.

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Turn o. all mobile phones and pagers during the examination.

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This is a closed book examination.

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You are advised to try the problems you feel more comfortable with .rst.

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Thereare9 multiplechoice questions. DO NOT guess wildly! If you do not have con.dence in your answer leave the answer box blank. Each incorrectly answered question will result in a 0.5 point deduction.

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For the short and long questions, you must show the working steps of your answers in order to receive all points.

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Unless stated otherwise, you may assume that all units are in SI system.

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Cheating is a serious o.ense. Students caught cheating are subject to a zero score as well as additional penalties.


Question No.
Points Out of
Q. 1-9
36
Q. 10-13
34
Q. 14
12
Q. 15
18
Total Points
100




Part I: Each correct answer in the answer box for the following 9 multiple choice ques-tions is worth 4 points. DO NOT guess wildly! If you do not have con.dence in your answer leave the answer box blank. Each incorrectly answered question will result in a
0.5 point deduction.
Question 123456789 Total Answer
1. Suppose that the population p(t) of certain .eld mice after t years from now is described by the initial value problem
dp

=0.5p.500 ,p(0)=800 .
dt Find thetime whenthepopulationjustbecome extinct; i.e.,thetime T (in years)when p(T)=0.
(a) 1.2476 (b) 1.8637 (c) 2.7645 (d) 3.2189 (e) 4.2537
2. For which of the following functions M(x,y)is the equation dy
M(x,y)+(x 3 +8y .3x)=0
dx
an exact equation?
22

(a) x(y2 +1) (b) 3y(x2 .1) (c) x2 .2y(d) x+ y (e) xy
3. By the method of undetermined coe.cients, there is a particular solution of the equation
5t
y .4y .5y =(1+2t2 .t3)e
which has the form u = p(t)e5t, where p(t)is a polynomial. The degree of p(t)is:

(a)1 (b)2 (c)3 (d)4 (e)5
4. Aperiodicexternalforce F(t)=9cos(t)is applied to a undamped spring-mass system so that the equation of motion of the mass is


2y +6y =9cos(t).
Which of the following values of will cause an unbounded oscillation(resonance) of the mass?


2

(a) 2 (b) 3 (c) 3 (d) (e) none of the above
33

.2t

5. Which of the following di.erential equations has ecos 3t and e.2t sin 3t as a pair of funda-mental solutions?

(a) y +2y +3y =0 (b) y .2y +3y =0 (c) y +2y .3y =0

(d) y +4y .7y =0 (e) y +4y +7y =0
6. The Wronskian W(y1,y2)(t)of a pair of fundame