(a) Explanation Procedure used: The solution to the DE with real, repetitive and distinct roots are y = c 1 e m 1 x + c 2 x e m 1 x and y = c 1 e m 1 x + c 2 e m 2 x , respectively. Calculation: The roots are m 1 = 3 , m 2 = − 5 and m 3 = 1 with multiplicity one, two and three. Thus, the roots are 3 , − 5 , − 5 , 1 , 1 , 1 . Hence, the auxiliary equation is ( m − 3 ) ( m + 5 ) 2 ( m − 1 ) 3 . Expand the above auxiliary equation. ( m − 3 ) ( m + 5 ) 2 ( m − 1 ) 3 = ( m − 3 ) ( m 2 + 25 + 10 m ) ( m 3 − 3 m 2 + 3 m − 27 ) = ( m 3 + 25 m + 10 m 2 − 3 m 2 − 75 − 30 m ) ( m 3 − 3 m 2 + 3 m − 27 ) = ( m 3 + 7 m 2 − 5 m − 75 ) ( m 3 − 3 m 2 + 3 m − 27 < (b) To determine To write: The solution of the homogeneous linear Cauchy Euler DE when m 1 = 3 , m 2 = − 5 and m 3 = 1 are roots of multiplicity one, two and three, respectively of an auxiliary equation.

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 3, Problem 11CR

(a)

To determine

To write: The solution of the homogeneous linear DE with constant coefficients when m1=3,m2=−5 and m3=1 are roots of multiplicity one, two and three, respectively of an auxiliary equation.

(b)

To determine

To write: The solution of the homogeneous linear Cauchy Euler DE when m1=3,m2=−5 and m3=1 are roots of multiplicity one, two and three, respectively of an auxiliary equation.

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Chapter 3, Problem 10CR

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Chapter 3 Solutions

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The solution of the homogeneous linear DE with constant coefficients when m 1 = 3 , m 2 = − 5 and m 3 = 1 are roots of multiplicity one, two and three, respectively of an auxiliary equation.

Solution Summary: The author explains the solution of the homogeneous linear DE with constant coefficients.