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Unformatted text preview: Math 2700, Fall 2011, Practice Sheet for Exam 1 Find general analytic solutions to the following differential equations. 1. dy dt = y + t 2. dy dt = 4 y- e 3 t 3. dy dt = e t y- 3 e t Modeling: 4. Consider a island with populations of grasses, horses, donkeys, and mules. Suppose that (1) horses eat grass to produce more horses. without grass, they die out (2) donkeys eat grass to produce more donkeys. without grass, they die out (3) horses mate with donkeys to produce mules (4) mules eat grass, but cant reproduce, and by themselves will die out (5) grasses grow by themselves, but have a maximum population size (the size of the island). grass is eaten by all the animals. Construct a plausable system of differential equations for the sizes of the various popula- tions as they change with time, subject to the above assumptions. 5. Suppose that we have populations of dogs and fleas and the following assumptions: (1) the dog populations will increase by itself. fleas might bite them, but it doesnt really(1) the dog populations will increase by itself....
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