sample-exam - y = x 2-y . 5. Solve the initial value...

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MAP 2302 Sample Exam I, Fall 2010 1. Does x 2 + y 2 = 4 determine a solution to the initial value problem dy dx = x y , y (0) = 2? 2. The initial value problem y 0 = 5 y 4 5 , y (0) = 0 has (choose the best answer): ( a ) a unique solution; ( b ) at least two solutions; or ( c ) no solution. 3. Consider the logistic equation p 0 = p ( p - 1)(2 - p ) (here p = p ( t ) is population (in thousands) where 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 2 ; and (c) Could a population of 900 ever increase to 1100? 4. Determine and draw some of the isoclines for
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Unformatted text preview: y = x 2-y . 5. Solve the initial value problem y-y x = xe x , y (1) = e-1 . 6. A tank initially contains 400 gallons of brine with 2 kilograms of salt. Suppose that brine in a concentration of . 3 kilogram salt per liter ows into the tank at a rate of 10 liters per minute and that the brine in the tank ows out at the same rate of 10 liters per minute. Write a dierential equation satised by A ( t ) equal to the kilograms of salt in the tank at time t...
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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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