Explanation Concept used: “ Complex roots of the characteristic equation : “Consider a second order differential equation, a y ″ + b y ′ + c y = 0 , where a , b and c are constants. Then, it’s characteristic equation with root r is, a r 2 + b r + c = 0 . Suppose the discriminant of the equation, D = b 2 − 4 a c is negative, then the roots of the characteristic equation are conjugate complex numbers denoted by, r 1 = λ + i μ and r 2 = λ − i μ where λ and μ are real.” Calculation: The given equation is, y ″ + 2 y ′ + 2 y = 0 . Obtain the general solution of the differential equation as follows. The characteristic equation of the given differential equation is, r 2 + 2 r + 2 = 0 . The discriminant of the characteristic equation is, D = b 2 − 4 a c = ( 2 ) 2 − 4 ( 1 ) ( 2 ) = − 4 Since, D < 0 , the roots of the equation are conjugate complex numbers. The roots of the equation, r 2 + 2 r + 2 = 0 is computed as follows

Elementary Differential Equations and Boundary Value Problems, Enhanced

11th Edition

ISBN: 9781119381648

Author: Boyce

Publisher: WILEY

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Chapter 3.3, Problem 7P

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To find: The general solution of the differential equation, y″+2y′+2y=0.

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Chapter 3.3, Problem 6P

Chapter 3.3, Problem 8P

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Chapter 3 Solutions

Elementary Differential Equations and Boundary Value Problems, Enhanced

Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P

Ch. 3.1 - Prob. 11P Ch. 3.1 - Prob. 12P Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - Prob. 15P Ch. 3.1 - Prob. 16P Ch. 3.1 - Prob. 17P Ch. 3.1 - Prob. 18P Ch. 3.1 - Prob. 20P Ch. 3.2 - Prob. 1P Ch. 3.2 - Prob. 2P Ch. 3.2 - Prob. 3P Ch. 3.2 - Prob. 4P Ch. 3.2 - Prob. 5P Ch. 3.2 - Prob. 6P Ch. 3.2 - Prob. 7P Ch. 3.2 - Prob. 8P Ch. 3.2 - Prob. 9P Ch. 3.2 - Prob. 10P Ch. 3.2 - Prob. 11P Ch. 3.2 - Prob. 12P Ch. 3.2 - Prob. 13P Ch. 3.2 - Prob. 14P Ch. 3.2 - Prob. 15P Ch. 3.2 - Prob. 16P Ch. 3.2 - Prob. 17P Ch. 3.2 - Prob. 18P Ch. 3.2 - Prob. 19P Ch. 3.2 - Prob. 20P Ch. 3.2 - Prob. 21P Ch. 3.2 - Prob. 22P Ch. 3.2 - Prob. 23P Ch. 3.2 - Prob. 24P Ch. 3.2 - Prob. 25P Ch. 3.2 - Prob. 26P Ch. 3.2 - Prob. 27P Ch. 3.2 - Prob. 28P Ch. 3.2 - Prob. 29P Ch. 3.2 - Prob. 30P Ch. 3.2 - Prob. 31P Ch. 3.2 - Prob. 32P Ch. 3.2 - Prob. 33P Ch. 3.2 - Prob. 34P Ch. 3.2 - Prob. 35P Ch. 3.2 - Prob. 36P Ch. 3.2 - Prob. 37P Ch. 3.2 - Prob. 38P Ch. 3.3 - Prob. 1P Ch. 3.3 - Prob. 2P Ch. 3.3 - Prob. 3P Ch. 3.3 - Prob. 4P Ch. 3.3 - Prob. 5P Ch. 3.3 - Prob. 6P Ch. 3.3 - Prob. 7P Ch. 3.3 - Prob. 8P Ch. 3.3 - Prob. 9P Ch. 3.3 - Prob. 10P Ch. 3.3 - Prob. 11P Ch. 3.3 - Prob. 12P Ch. 3.3 - Prob. 13P Ch. 3.3 - Prob. 14P Ch. 3.3 - Prob. 15P Ch. 3.3 - Prob. 16P Ch. 3.3 - Prob. 17P Ch. 3.3 - Prob. 18P Ch. 3.3 - Prob. 19P Ch. 3.3 - Prob. 20P Ch. 3.3 - Prob. 21P Ch. 3.3 - Prob. 22P Ch. 3.3 - Prob. 23P Ch. 3.3 - Prob. 24P Ch. 3.3 - Prob. 25P Ch. 3.3 - Prob. 26P Ch. 3.3 - Prob. 27P Ch. 3.3 - Prob. 28P Ch. 3.3 - Prob. 29P Ch. 3.3 - Prob. 30P Ch. 3.3 - Prob. 31P Ch. 3.3 - Prob. 32P Ch. 3.3 - Prob. 33P Ch. 3.3 - Prob. 34P Ch. 3.3 - Prob. 35P Ch. 3.3 - Prob. 36P Ch. 3.4 - Prob. 1P Ch. 3.4 - Prob. 2P Ch. 3.4 - Prob. 3P Ch. 3.4 - Prob. 4P Ch. 3.4 - Prob. 5P Ch. 3.4 - Prob. 6P Ch. 3.4 - Prob. 7P Ch. 3.4 - Prob. 8P Ch. 3.4 - Prob. 9P Ch. 3.4 - Prob. 10P Ch. 3.4 - Prob. 11P Ch. 3.4 - Prob. 12P Ch. 3.4 - Prob. 13P Ch. 3.4 - Prob. 14P Ch. 3.4 - Prob. 15P Ch. 3.4 - Prob. 16P Ch. 3.4 - Prob. 17P Ch. 3.4 - Prob. 18P Ch. 3.4 - Prob. 19P Ch. 3.4 - Prob. 20P Ch. 3.4 - Prob. 21P Ch. 3.4 - Prob. 22P Ch. 3.4 - Prob. 23P Ch. 3.4 - Prob. 24P Ch. 3.4 - Prob. 25P Ch. 3.4 - Prob. 26P Ch. 3.4 - Prob. 27P Ch. 3.4 - Prob. 28P Ch. 3.4 - Prob. 29P Ch. 3.4 - Prob. 30P Ch. 3.4 - Prob. 31P Ch. 3.4 - Prob. 32P Ch. 3.4 - Prob. 33P Ch. 3.4 - Prob. 34P Ch. 3.5 - Prob. 1P Ch. 3.5 - Prob. 2P Ch. 3.5 - Prob. 3P Ch. 3.5 - Prob. 4P Ch. 3.5 - Prob. 5P Ch. 3.5 - Prob. 6P Ch. 3.5 - Prob. 7P Ch. 3.5 - Prob. 8P Ch. 3.5 - Prob. 9P Ch. 3.5 - Prob. 10P Ch. 3.5 - Prob. 11P Ch. 3.5 - Prob. 12P Ch. 3.5 - Prob. 13P Ch. 3.5 - Prob. 14P Ch. 3.5 - Prob. 15P Ch. 3.5 - Prob. 22P Ch. 3.5 - Prob. 23P Ch. 3.5 - Prob. 24P Ch. 3.5 - Prob. 25P Ch. 3.5 - Prob. 26P Ch. 3.5 - Prob. 27P Ch. 3.5 - Prob. 28P Ch. 3.5 - Prob. 29P Ch. 3.5 - Prob. 30P Ch. 3.6 - Prob. 1P Ch. 3.6 - Prob. 2P Ch. 3.6 - Prob. 3P Ch. 3.6 - Prob. 4P Ch. 3.6 - Prob. 5P Ch. 3.6 - Prob. 6P Ch. 3.6 - Prob. 7P Ch. 3.6 - Prob. 8P Ch. 3.6 - Prob. 9P Ch. 3.6 - Prob. 10P Ch. 3.6 - Prob. 11P Ch. 3.6 - Prob. 12P Ch. 3.6 - Prob. 13P Ch. 3.6 - Prob. 14P Ch. 3.6 - Prob. 15P Ch. 3.6 - Prob. 16P Ch. 3.6 - Prob. 17P Ch. 3.6 - Prob. 18P Ch. 3.6 - Prob. 19P Ch. 3.6 - Prob. 20P Ch. 3.6 - Prob. 21P Ch. 3.6 - Prob. 22P Ch. 3.6 - Prob. 23P Ch. 3.6 - Prob. 24P Ch. 3.6 - Prob. 25P Ch. 3.6 - Prob. 26P Ch. 3.7 - Prob. 1P Ch. 3.7 - Prob. 2P Ch. 3.7 - Prob. 3P Ch. 3.7 - Prob. 4P Ch. 3.7 - Prob. 5P Ch. 3.7 - Prob. 6P Ch. 3.7 - Prob. 7P Ch. 3.7 - Prob. 8P Ch. 3.7 - Prob. 9P Ch. 3.7 - Prob. 10P Ch. 3.7 - Prob. 11P Ch. 3.7 - Prob. 12P Ch. 3.7 - Prob. 13P Ch. 3.7 - Prob. 14P Ch. 3.7 - Prob. 15P Ch. 3.7 - Prob. 16P Ch. 3.7 - Prob. 17P Ch. 3.7 - Prob. 18P Ch. 3.7 - Prob. 19P Ch. 3.7 - Prob. 20P Ch. 3.7 - Prob. 21P Ch. 3.7 - Prob. 22P Ch. 3.7 - Prob. 23P Ch. 3.7 - Prob. 24P Ch. 3.8 - Prob. 1P Ch. 3.8 - Prob. 2P Ch. 3.8 - Prob. 3P Ch. 3.8 - Prob. 4P Ch. 3.8 - Prob. 5P Ch. 3.8 - Prob. 6P Ch. 3.8 - Prob. 7P Ch. 3.8 - Prob. 9P Ch. 3.8 - Prob. 11P Ch. 3.8 - Prob. 14P

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The general solution of the differential equation, y ″ + 2 y ′ + 2 y = 0 .

To find: The general solution of the differential equation, y″+2y′+2y=0.

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Chapter 3 Solutions