And r3(4) «The auxiliary equation of y"" - 4y" - 4y' + 16y = 0 isr³ − 4r² − 4r + 16 = 0. The auxiliary equation has a root in the interval[-0.75,3.75].Let f(r) = r³ - 4r² - 4r + 16, so that the roots of the auxiliary equationcan be determined by solving f(r) = 0.Then, applying four iterations of the Bisection Method to f(r), usingthe initial approximations r₁= -0.75 and r2 = 3.75, gives the followingapproximations for the root in [-0.75, 3.75]:(¹1) = [(2)131333)=(64)

The solution of an equation fr=0 is defined as the values of r which satisfies the differential…

Answered: The auxiliary equation of y"" - 4y" -…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.1: Solutions Of Elementary And Separable Differential Equations

Problem 2YT

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The auxiliary equation of of y'''-4y''-4y'+16y=0 is r^(3)-4r^(2)-4r+16=0 . The auxiliary equation has a root in the interval [3,6]. Let f(r)=r^(3) -4r^(2)-4r+16 , so that the roots of the auxiliary equation can be determined by solving f(r)=0 . Then, applying four iterations of the Bisection Method to f(r) , using the initial approximations r1=3 and r2=6 , gives the following approximations for the root in [3,6]: r3^(1)= r3^(2)= r3^(3)= r3^(4)=
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