sample-exam_001 - 3. Solve the initial value problem t 2...

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MAP 2302 sample Exam I, Spring 2011 1. In each case, determine if the initial value problem has a unique solution (give expla- nations). (a) y 0 = 5 y 4 5 , y (0) = 0; (b) y 0 = y 4 - x 4 , y (0) = 7. 2. Consider the logistic equation p 0 = 3 p - 2 p 2 (here p = p ( t ) is population (in thousands) and t is time). (a) Sketch the direction field; (b) Find the limit as t tends to infinity of the solution to the di±erential equation with initial condition p (0) = 3; and (c) Could a population of 2000 ever decrease to 800? Explain.
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Unformatted text preview: 3. Solve the initial value problem t 2 x-3 tx = 1 , x (2) = 0 . 4. Solve the initial value problem, y = 3 x 2 +4 x +2 2 y +1 , y (0) =-1. 5. Write a di±erential equation to model the statement: The velocity of a particle moving along a straight line is proportional to the fourth power of its position x ....
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This note was uploaded on 12/15/2011 for the course MAP 2302 taught by Professor Tuncer during the Spring '08 term at University of Florida.

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