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Unformatted text preview: HKUST MATH 152 Applied Linear Algebra and Differential Equations MidTerm Examination Name: 19th March 2005 Student I.D.: 13:00–15:30 Tutorial Section: Directions: • Do NOT open the exam until instructed to do so. • All mobile phones and pagers should be switched off during the examination. • Please write your name, ID number, and Section in the space provided above. • Answer ALL questions. You are advised to try the problems you feel more comfortable with first. • This is a closed book examination. • No graphical calculators are allowed. • You may write on both sides of the examination papers. • Once you are allowed to open the exam, please check that you have 10 pages in addition to this cover page. • For answering Part II, you must show all your working steps in order to receive full marks. • Cheating is a serious offense. Students who commit this offense may receive zero mark in the examination. However, more serious penalty may be imposed. Question No. Marks Out of Q. 116 32 Q. 17 8 Q. 18 4 Q. 19 8 Q. 20 8 Q. 21 8 Q. 22 8 Q. 23 8 Q. 24 8 Q. 25 8 Total Marks 100 1 Part I: Answer each of the following 16 multiple choice questions. Each correct answer is worth 2 marks. Question 1 2 3 4 5 6 7 8 9 10 Answer Question 11 12 13 14 15 16 Total Answer 1. The function y = e t is a solution of the differential equation (a) 2 y 000 2 y 00 9 y + 9 y = 0 (b) y 00 + y = 2 e t (c) 4 t 2 y 00 + 8 ty + y = 0 (d) ty 00 + ( t + 1) y + y = 0 (e) y 00 + y = 0 2. Find a fundamental set of solutions for 2 y 00 + 5 y 3 y = 0 . (a) e 1 2 t , e 3 t (b) e 3 t , e 2 t (c) e 3 t , e 1 2 t (d) e 1 2 t , 1 (e) e 1 2 t e 3 t , e 1 2 t + e 3 t 3. Find the integrating factor that can be used to solve the following firstorder equation dr dθ + r tan θ = cos 2 θ, < θ < π 2 . (a) sin θ (b) cos θ (c) tan θ (d) sec θ (e) csc θ 4. The following equation is not exact but becomes exact when multiplied by the integrating factor. ( 3 xy + y 2 ) dx + ( x 2 + xy ) dy = 0 ....
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This note was uploaded on 09/30/2010 for the course MATH MATH152 taught by Professor Kcc during the Spring '10 term at HKUST.
 Spring '10
 KCC
 Math, Linear Algebra, Algebra, Equations

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