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Unformatted text preview: MATH 138 Assignment 4 Spring 2009 Differential Equations: direction fields, separable equations, linear equations and applications. Submit all problems marked (*) and the Maple Lab question by 12:30 p.m. on Friday, June 5. 1. Verify that y ( x ) = cos( x )(sin( x )- 1) is a solution of the initial value problem y + (tan x ) y = cos 2 ( x ) y (0) = 1 on the interval (- 2 , 2 ). 2. (a) ( * ) Find the values of k such that y ( t ) = cos( kt ) is a solution of the differential equation 4 y 00 =- 25 y . (b) ( * ) For those values of k , verify that every member of the family y ( t ) = A sin( kt )+ B cos( kt ) is also a solution. 3. ( * ) A function y ( t ) satisfies the differential equation dy dt = y 3- 6 y 2 + 5 y. (a) Find the constant solutions of the equation. (b) For what values of y is y increasing? and decreasing? (Do not try to solve the differential equation!) 4. Find the equation of the curve satisfying the differential equation y 00 = (2 + x )(2- x ) which passes through the point (1...
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