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Unformatted text preview: NAME Quiz II
y 1. a) The differential form = (ln y + x  1)dx + (ln x + x  1)dy is exact in any y rectangle contained in the first quadrant (where x > 0 and y > 0). Find a function F (x, y) defined in the first quadrant such that dF = . b) The level curves of the function F (x, y) that you found in part a) are solutions to a first order differential equation. Write down that differential equation. 2 2. A tank contains 40 gallons of pure water. Starting at time zero, a saltwater solution containing 0.5 lb/gal of salt enters the tank at a rate of 2 gal/min. At the same time a drain is opened at the bottom of the tank allowing the saltwater solution to leave at a rate of 2 gal/min. Assume that the solution is kept perfectly mixed at all times. How long will it take for the amount of salt in the tank to reach 5 lbs? Leave your answer in exact form (in terms of logarithms). ...
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 Spring '07
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 Differential Equations, Equations, Derivative, Differential form, De Rham cohomology

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