Explanation Use the given equation to be rewritten in the linear form and use the integrating factor to determine the solution . Given: a , b , r are constants. Calculation: Given d y d t = − k ( y − a − b sin r t ) Rewriting this gives d y d t + k y = k ( a + b sin r t ) The integrating factor is then e k t , Multiplying this with the integrating factor gives ( e k t y ) ' = k a e k t + k b e k t sin r t We use integration by parts to find the integral value of the second part of the above equation...

4th Edition

ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Differential Equations

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Chapter 10.5, Problem 45E

To determine

To show that $y = C e^{- k t} + a + b k (\frac{k \sin r t - r \cos r t}{k^{2} + r^{2}})$ is a general solution of $\frac{d y}{d t} = - k (y - a - b \sin r t)$ .

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Chapter 10.5, Problem 44E

Chapter 10.5, Problem 46E

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Which of the functions shown below is differentiable at = 0? Select the correct answer below: -7-6-5-4- -6-5-4-3-21, -7-6-5-4-3-2 -7-6-5-4-3-2-1 2 4 5 6 -1

correct answer is Acould you please show me how to compute using the residue theorem

Chapter 10 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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To show that y = C e − k t + a + b k ( k sin r t − r cos r t k 2 + r 2 ) is a general solution of d y d t = − k ( y − a − b sin r t ) .

Solution Summary: The author explains how the given equation is rewritten in the linear form and uses the integrating factor to determine the solution.

Concept explainers

Videos

To show that $y = C e^{- k t} + a + b k (\frac{k \sin r t - r \cos r t}{k^{2} + r^{2}})$ is a general solution of $\frac{d y}{d t} = - k (y - a - b \sin r t)$ .

Want to see the full answer?

Chapter 10 Solutions

To show that y = C e − k t + a + b k ( k sin r t − r cos r t k 2 + r 2 ) is a general solution of d y d t = − k ( y − a − b sin r t ) .

Solution Summary: The author explains how the given equation is rewritten in the linear form and uses the integrating factor to determine the solution.

Concept explainers

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To show that y=Ce−kt+a+bk(ksinrt−rcosrtk2+r2) is a general solution of dydt=−k(y−a−bsinrt).

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Chapter 10 Solutions

To show that $y = C e^{- k t} + a + b k (\frac{k \sin r t - r \cos r t}{k^{2} + r^{2}})$ is a general solution of $\frac{d y}{d t} = - k (y - a - b \sin r t)$ .