M251ex1(sp10)

# M251ex1(sp10) - MATH 251 Name Examination I Student Number...

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MATH 251 Examination I February 25, 2010 FORM A 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. 1 / 2 : 3 thru 11: 12: 13: 14: Total: Do not write in this box.

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MATH 251 EXAMINATION I February 25, 2010 1. (12 points) Consider the diﬀerential equation t 2 + 2 t - 1 - 4 y y 0 = 0 . Answer the following questions. (a) (2 points) What is the order of this equation? (b) (2 points) Is this equation linear? (c) (2 points) Is this equation separable? (d) (2 points) Is this equation exact? (e) (4 points) Find its general solution. You may leave your answer in an implicit form. 2. (4 points) Find a suitable integrating factor that could be used to solve the equation below. ty 0 - 4 t 2 y = t 3 e 9 t tan( πt ) , t > 0 . Page 2 of 10
MATH 251 EXAMINATION I February 25, 2010 3. (5 points) Suppose the velocity v ( t ) of a speedboat is given by the equation v 0 = 200 - 1 2 v 2 , v 0 . What is its limiting velocity, lim

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M251ex1(sp10) - MATH 251 Name Examination I Student Number...

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