Homework-2 - (Problem 2-4, specially assigned) Compute the...

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1 Homework 2 Assignment Date: Wednesday (09/14/2009) Collection Date: Wednesday (09/23/2009) Grade: 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: ݕ ൌ1൅ݔ൅ݕ൅ݔݕ (Problem 2-2, Prob 25, P. 43, 4e) Find the explicit particular solution of the initial value problem ݔݕ െݕൌ2ݔ ݕ ݕሺ1ሻൌ1 (Problem 2-3, Prob 13, P. 56, 4e) Solve the following differential equation. Primes denote derivatives with respect to x. ݀ݕ ݀ݔ ൅ݕൌ݁ ݕሺ0ሻൌ1
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Unformatted text preview: (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. (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 constant k=5 and the initial population ܲ ଴ ൌ 100 . Compute the time when you would have 200, 300, 500 mice....
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This note was uploaded on 08/08/2010 for the course AMS 361 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.

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