Homework-2-Solution - AMS 361 Applied Calculus IV(DE&...

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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 2-1, 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 2-2, Prob 25, P. 43, 4e) Find the explicit particular solution of the initial value problem 2 1 1 2 1 1 1 (Problem 2-3, Prob 13, P. 56, 4e) Solve the following differential equation. Primes denote derivatives with respect to x. 0 1 1 2 (Problem 2-4, specially assigned) Compute the time needed to empty a fully-filled spherical tank of inner radius R and leaking constant is k. Also, please compute the time to drain the top hemi-sphere 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 2-5, 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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