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Unformatted text preview: HKUST MATH 152 Applied Linear Algebra and Differential Equations MidTerm Examination Name: 22nd October 2005 Student ID: 10:00–12:30 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. 115 30 Q. 16 6 Q. 17 8 Q. 18 8 Q. 19 8 Q. 20 8 Q. 21 8 Q. 22 8 Q. 23 8 Q. 24 8 Total Marks 100 1 Part I: Answer each of the following 15 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 Total Answer 1. Which one of the following equations is solvable by the method of integrating factor? (a) dy dt + ty = y 2 (b) dy dt = 2 ty t 2 + 2 y (c) y = t 2 + 1 y (d) dy dt 2 y + 1 2 t = 2 t + 1 2 y (e) y 00 + 4 y 5 y = 0 2. Consider the initial value problem y 00 y + 1 4 y = 0 , y (0) = 1 , y (0) = b. Find the critical value of b that distinguishes y ( t ) grows positively and negatively, as t → ∞ . (a) 1 4 (b) 1 2 (c) 1 (d) 2 (e) 4 3. The velocity v ( t ) of a falling object satisfies the initial value problem dv dt + 0 . 2 v = 9 . 8 , v (0) = 0 . Find the time that must elapse for the object to reach 98% of its limiting velocity. (a) 5ln50 (b) 25ln10 (c) 50ln5 (d) 25 (e) 50 4. Determine the value of b which makes the following differential equation exact. ( x + ye 2 xy ) dx + bxe 2 xy dy = 0 . (a) 1 (b) 2 (c) 3 (d) 4 (e) 5 2 5. The thirdorder differential equation x 000 + 3 x 00 + 2 x 5 x = sin2 t can be converted to a system of three firstorder equations. They are (a) x 1 = x 2 + x 3 , x 2 = x 1 x 3 , x 3 = x 1 x 2 3 x 3 + sin2 t (b) x 1 = x 2 , x 2 = 2 x 3 , x 3 = x 1 3 x 2 + sin2 t (c) x 1 = x 2 x 3 , x 2 = x 3 x 1 , x 3 = 3 x...
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 Spring '10
 KCC
 Math, Linear Algebra, Algebra, Equations

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