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Unformatted text preview: MATH 251 Examination I February 28, 2008 Name: Student Number: Section: This exam has 13 questions for a total of 100 points. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not supported by work. The point value for each question is in parentheses to the right of the question number. You may not use a calculator on this exam. Please turn off and put away your cell phone. 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: Total: Do not write in this box. MATH 251 EXAMINATION I February 28, 2008 1. (6 points) For each of the differential equations below state its order and whether it is linear or nonlinear. Equation order linear/nonlinear (i) 2 y ′′′ + ty ′′ − y ′ + e t y = 0 (ii) y ′ = y 2 − y ′′ (iii) y ′ − cos(2 t ) y = t 2 − e − 5 t 2. (5 points) Which of the following initial value problems below is guaranteed to have a unique solution according to the appropriate Existence and Uniqueness Theorem? (a) y ′ + ln( t ) y = 2 , y (0) = 1 (b) cos( t ) y ′ − 5 y = t 2 , y ( π 2 ) = 0 (c) y ′′ + 9 y = 1 1 − e t , y (0) = 2 , y ′ (0) = − 2 (d) y ′′ + ( t 2 + 1) y ′ + t 3 y = 0 , y (1) = − 1 , y ′ (1) = 0 Page 2 of 10 MATH 251 EXAMINATION I February 28, 2008 3. (5 points) Consider the second order linear equation with constant coefficients ay ′′ + by ′ + cy = 0 , a negationslash = 0 ....
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, Boundary value problem

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