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math3c-01-W08-5..

math3c-01-W08-5.. - AUBREY MCMILLAN WeBWorK problems...

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AUBREY MCMILLAN Math 3C, Section 2, Winter 2006 WeBWorK problems. WeBWorK assignment DELA 1 2 due 3/4/08 at 11:59 PM. 1. (1 pt) Select the functions from the list that solve these dif- ferential equations. A. y = 2tan ( 2 t ) B. y = 3 t + t 2 C. y = t 2 ln ( t ) D. y = t R 0 e - 2 ( s 2 - t 2 ) ds E. y = e - t 2 - e - 3 t F. y = t + t 2 + 2 e 2 t 1. y 0 = y 2 + 4 ( | t | < π / 4 ) 2. y 0 = 1 t y + t ( t > 0 ) 3. y 0 = 2 y + 1 - 2 t 2 2. (1 pt) Observe that y = ce t 2 is a solution, for any real c , of y 0 = 2 ty . Determine c so that y (0) = 2. c = 3. (1 pt) Select the functions from the list that solve these dif- ferential equations. A. y = 2 tan ( 2 t ) B. y = 3 t + t 2 C. y = t 2 ln ( t ) D. y = t R 0 e - 2 ( s 2 - t 2 ) ds E. y = e - t 2 - e - 3 t F. y = t + t 2 + 2 e 2 t 1. y 0 = 2 y + 1 - 2 t 2 2. y 0 = 1 t y + t ( t > 0 ) 3. y 0 + 3 y = e - t 4. (1 pt) Observe that y = Ae 2 t + Be - t is a solution, for any real A and B , of y 00 - y 0 - 2 y = 0 . Determine A and B so that the solution of the DE satisfies both y ( 0 ) = 2 and y 0 ( 0 ) = - 5 . A = B = 5. (1 pt) Logistic Population Model The simplest case of the logistic model is represented by the DE y 0 = ky ( 1 - y ) , where it k ¿ 0 is the growth constant. The
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