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# MATH 238 Quiz: Dropbox Homework 6 (annotated).51639785.1475280966936 Premium

2 Pages
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School
University of Alabama
Department
Mathematics
Course
MATH 238
Professor
Huy Duc Vo
Semester
Spring

Description
Dropbox Homework 6 -2 3 -2 25y” + 20y’+4y=0; y(5) =4e , y’(5) =- e a)Obtain the general solution of the differential equation Let y” and y’ correspond to r and r; The auxiliary equation is: 25r +20r+4 =0 (5r+2) = 0 2 2 r = - ,‒5 = -0.4, -0.4 The general solutiony = c1e-0.4x+ c 2e -0.4x b)Impose initial conditions to obtain the unique solution of the initial value problem -0.4x -0.4x y = c1e + c2xe substitute y= 4e , x= 5 -2 -2 -2 ▯ 4e = c 1 + c 2e ▯ c 15c 2 4 Substitute 2
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