Unformatted text preview: AMS 361: Applied Calculus IV (DE & BVP)
Homework 2
Assignment Date: Collection Date: Grade: Wednesday (09/14/2009) Wednesday (09/23/2009) Each problem is worth 10 points (Problem 21, Prob 17, P. 43, 4e) Find the general solutions (implicit if necessary, explicit if convenient) of the differential equations in the following problem: 1 1 1 1 1 1 ln 1 1 1 1 1 (Problem 22, Prob 25, P. 43, 4e) Find the explicit particular solution of the initial value problem 2 1 1 2 1 1 1 (Problem 23, Prob 13, P. 56, 4e) Solve the following differential equation. Primes denote derivatives with respect to x. 0 1 1 2 (Problem 24, specially assigned) Compute the time needed to empty a fullyfilled spherical tank of inner radius R and leaking constant is k. Also, please compute the time to drain the top hemisphere with the same parameters R and k. Of course, in the latter case, the hole is at the equator of the sphere. Part A 2 2 2 = 2 2 0
√ 2 Part B Follow the same procedure as above
√ 2 2 5 2 8 5 2 5 8 5 0 3 (Problem 25, specially assigned) A giant mouse cage that allow M=1000 mice to survive for long term, i.e., the containing capacity is M=1000. Now, we assume the population of nice follows the logistics equation with a 100. Compute the time when constant k=5 and the initial population you would have 200, 300, 500 mice. 1000; 5; 100 200 300 500 9.2103 9.6158 10.1266 4 ...
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 Fall '08
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 Derivative, BVP, explicit particular solution

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