M251ex1(su10)

M251ex1(su10) - MATH 251 Examination I Name Student Number...

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MATH 251 Examination I July 6, 2010 Name: Student Number: Section: This exam has 14 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. For other problems, points might be deducted, at the sole discretion of the instructor, for an answer not supported by a reasonable amount of 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. Problem # Score Maximum 1-8: 47 points 9: 8 points 10: 8 points 11: 12 points 12: 10 points 13: 8 points 14: 7 points Total: 100 points

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MATH 251 EXAMINATION I July 06, 2010 Multiple Choice Section 1. (8 points) Classify the following diﬀerential equations in terms of (i) Order (ii) Linear or Nonlinear Order Linear/nonlinear y 0 ( t ) = ty 2 ( t ) y 00 ( t ) = ln( t ) y ( t ) ty ( t ) y 0 ( t ) y 00 ( y ) - 1 = 0 u xy ( x,y ) = 0 2. (5 points) Consider the initial value problem ( t 2 - 16) y 0 - ln( t - 1) y = sin 3 t, y ( π ) = 5 . Without solving the equation, what is the largest interval in which a unique solution is guaranteed to exist? (a) ( - 4 , 4) (b) (1 , ) (c) (1 , 4) (d) (4 , ) Page 2 of 12
MATH 251 EXAMINATION I July 06, 2010 3. (5 points) What is the general solution of the following diﬀerential equation y 00 ( t ) + 2 y 0 ( t ) - 3 y ( t ) = 0 (a) y ( t ) = C 1 e - t + C 2 e t (b) y

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M251ex1(su10) - MATH 251 Examination I Name Student Number...

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