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m345t1S11-1 - MA 345 Dierential Equations Name Spring 2011...

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MA 345 Di ff erential Equations Spring 2011 Exam I Dr. E. Jacobs Name : Score : Problems 1 - 5 require that you show all work. All answers must be expressed in simplest form. Do your calculations on the blank sheets provided. The papers will be stapled together at the end of the test. 1. (12 points) Find the solution of the following di ff erential equation. Show all work. dy dx = - 2 xy 1 + x 2 y (0) = 2 2. (12 points) Find the solution of the following di ff erential equation. Show all work. dy dx + 2 xy = e - x 2 y (0) = 0 3. (16 points) A swimming pool whose volume is 40,000 liters is filled with pure water. Starting at t = 0, water containing 1 2 gram of chlorine per liter is pumped into the pool at the rate of 8 liters per minute. Pool water flows out at 8 liters per minute also. Let x ( t ) be the number of grams of chlorine in the pool after t minutes. a) Set up an appropriate di ff erential equation for x ( t ) b) Solve the equation. Show all work. Determine the values of any constants that appear in your solution.
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