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AMATH-250-1059-Final_exam[1]

# AMATH-250-1059-Final_exam[1] - UNIVERSITY OF WATERLOO FINAL...

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UNIVERSITY OF WATERLOO FINAL EXAMINATION FALL TERM 2005 COURSE NUMBER AMATH 250 COURSE TITLE Introduction to Differential Equations DATE OF EXAM Tuesday December 20, 2005 TIME PERIOD 9:00 a.m. - 11:30 p.m. DURATION OF EXAM 2 1 2 hours NUMBER OF EXAM PAGES (including this cover sheet) 10 pages INSTRUCTOR B. Marshman EXAM TYPE Closed book ADDITIONAL MATERIALS ALLOWED NO AIDS Name ID No. Instructions: 1. It is important that your conclusions be justified and that your solutions be well- organized. 2. Use the reverse side of page if necessary. Questions Mark Out of 1 15 2 13 3 12 4 20 5 14 6 14 7 12 Total 100

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AMATH 250 - Final Examination Fall 2005 1. a) (i) Find the general solution of the DE y = 3 x 2 (1 - y ). [15] (ii) Sketch the family of solutions, indicating any equilibrium solutions, and in- cluding the solutions for which y (0) = 2 , y (0) = 0, and y (0) = - 2. b) (i) Solve the I.V.P. y = - 2 x y + x, y (1) = 0, and state the domain of the solution.
AMATH 250 - Final Examination Fall 2005 2. At time t = 0, a group of N 0 students returns to campus from a tropical holiday, [13] infected with a flu virus (to which none of the remaining students is immune). The number N ( t ) of infected students grows rapidly according to the model dN dt = 0 . 01 N 1 - N 2000 , N (0) = N 0 (a) Use direction field analysis

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AMATH-250-1059-Final_exam[1] - UNIVERSITY OF WATERLOO FINAL...

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