Explanation The given differential equation is d Q d t = r ( a + b Q ) , Q ( 0 ) = Q 0 . Rewrite the differential equation is d Q d t = r ( a + b Q ) as follows. d Q ( a + b Q ) = r d t Integrate both side of the above equation as follows: ∫ d Q ( a + b Q ) = ∫ r d t ln ( a + b Q ) b = r t + c ln ( a + b Q ) = b r t + C [ C = b c ] a + b Q = e b r t + C Simplify further as, a + b Q = e b r t e C Substitute Q ( 0 ) = Q 0 in a + b Q = e b r t e C

Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion

11th Edition

ISBN: 9781119336617

Author: William E. Boyce, Richard C. DiPrima

Publisher: Wiley (WileyPLUS Products)

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Chapter 2.2, Problem 24P

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To solve: The differential equation dQdt=r(a+bQ),Q(0)=Q0 and explain how solution behaves as t→∞.

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Chapter 2.2, Problem 23P

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Chapter 2 Solutions

Elementary Differential Equations and Boundary Value Problems, 11e WileyPLUS Registration Card + Loose-leaf Print Companion

Ch. 2.1 - Prob. 1P Ch. 2.1 - Prob. 2P Ch. 2.1 - Prob. 3P Ch. 2.1 - Prob. 4P Ch. 2.1 - Prob. 5P Ch. 2.1 - Prob. 6P Ch. 2.1 - Prob. 7P Ch. 2.1 - Prob. 8P Ch. 2.1 - Prob. 9P Ch. 2.1 - Prob. 10P

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The differential equation d Q d t = r ( a + b Q ) , Q ( 0 ) = Q 0 and explain how solution behaves as t → ∞ .

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To solve: The differential equation dQdt=r(a+bQ),Q(0)=Q0 and explain how solution behaves as t→∞.

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Chapter 2 Solutions