m260hw1 - Differential Equations Homework Assignment 1 Due...

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Unformatted text preview: Differential Equations Homework Assignment 1 Due on Thursday, January 20, at the start of the recitation you are registered in Your homework should have a cover sheet with the following information: course title, recitation, last and first name (as they appear in the roster), number of homework. If you use several sheets, please staple them. The problems should be written neatly and in the order they were assigned. Problem 1. Draw a direction field for the given differential equation. Based on the direction field, determine the behavior of the solution as t → ∞. Describe how this behavior depends on the initial value of y at t = 0. dy = (y − 1)(y − 3). dt Problem 2. Solve the given initial value problem. y= t2 , y + t3 y y (0) = −2. Problem 3. A 5-gallon bucket is full of pure water. Suppose we begin dumping salt into the bucket at a rate of 1/4 pounds per minute. Also, we open the spigot so that 1/2 gallons per minute leaves the bucket, and we add pure water to keep the bucket full. If the saltwater solution is always well mixed, what is the amount of salt in the bucket after t minutes? What is the amount of salt in the bucket as t → ∞? ...
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This note was uploaded on 09/08/2011 for the course MATH 21-260 taught by Professor Tolle during the Spring '07 term at Carnegie Mellon.

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