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Unformatted text preview: 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. MATH 251 Exam I 1. (16 points) Consider the general nth order ordinary differential equation F ( t, y ( t ) , y ( 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 nonlinear, 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 + 2 y = 0 y...
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations, 1%, Boundary value problem, 10 gallons

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