Explanation Given: a n = 7 a n − 1 − 16 a n − 2 + 12 a n − 1 + n 4 n … i Formula used: If the characteristic equation of a n = 7 a n − 1 − 16 a n − 2 + 12 a n − 1 + n 4 n has roots p , q ( r e p e a t e d t w i c e ) , then The general solution of the homogeneous equation is given by α p n + β q n + γ n q n … i i Calculation: The characteristic equation of a n = 7 a n − 1 − 16 a n − 2 + 12 a n − 1 + n 4 n is x 3 − 7 x 2 + 16 x − 12 = x − 3 x − 2 x − 2 = 0 So, applying ( ii ), the general solution of the homogeneous equation is α 3 n + β 2 n + γ n 2 n

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

8th Edition

ISBN: 9781259676512

Author: Kenneth H Rosen

Publisher: McGraw-Hill Education

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Chapter 8.2, Problem 34E

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Find the solution of the recurrence equation

an=7an−1−16an−2+12an−1+n4n With initial conditions a0=−2,a1=0,a2=5

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Chapter 8.2, Problem 33E

Chapter 8.2, Problem 35E

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Chapter 8 Solutions

Discrete Mathematics and Its Applications ( 8th International Edition ) ISBN:9781260091991

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Find the solution of the recurrence equation a n = 7 a n − 1 − 16 a n − 2 + 12 a n − 1 + n 4 n With initial conditions a 0 = − 2 , a 1 = 0 , a 2 = 5

Solution Summary: The author explains how to find the solution of the recurrence equation a_n.

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Find the solution of the recurrence equation

an=7an−1−16an−2+12an−1+n4n With initial conditions a0=−2,a1=0,a2=5

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Chapter 8 Solutions

Find the solution of the recurrence equation a n = 7 a n − 1 − 16 a n − 2 + 12 a n − 1 + n 4 n With initial conditions a 0 = − 2 , a 1 = 0 , a 2 = 5

Solution Summary: The author explains how to find the solution of the recurrence equation a_n.

Videos

Find the solution of the recurrence equation an=7an−1−16an−2+12an−1+n4n With initial conditions a0=−2,a1=0,a2=5

Want to see the full answer?

Chapter 8 Solutions

Find the solution of the recurrence equation

an=7an−1−16an−2+12an−1+n4n With initial conditions a0=−2,a1=0,a2=5