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M251ex1(fa00)

# M251ex1(fa00) - Name MATH 251 Midterm Exam I Sept 26 2000...

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MATH 251 Midterm Exam I Sept. 26, 2000 Name: Student Number: Instructor: Section: There are 6 partial credit questions. In order to obtain full credit for partial credit problems, all work must be shown. Credit will not be given for an answer not sup- ported by work. THE USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINATION. At the end of the examination, the booklet will be collected. Time Limit: 75 minutes 1: 2: 3: 4: 5: 6: Total: Do not write in this box.

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MATH 251 Exam I 1. (16 points) Consider the general n-th order ordinary differential equation F ( t, y ( t ) , y 0 ( t ) , ..., y ( n ) ( t )) = 0 (a) What general form must F have for the equation to be linear? (b) Classify the following equations as linear or non-linear, and state their order. (i) t d 2 y dt 2 + t 2 dy dt + t 3 y = cos( t ) (ii) t d 3 y dt 3 + t 2 dy dt + t 3 y = cos( y ) (iii) dy dx = 2 y - 3 2 x +2 Page 2 of 7
MATH 251 Exam I 2. (16 points) (a) Find the solution to the initial value problem y 00 + 3 y 0 + 2 y = 0 y (0) = 0 y 0 (0) = α (b) For what value(s) of α is the lim t →∞ y ( t ) = 0?

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M251ex1(fa00) - Name MATH 251 Midterm Exam I Sept 26 2000...

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