The solution of the Integro - differential equation ϕ ′ ( t ) + ∫ 0 t ( t − ξ ) ϕ ( ξ ) d ξ = t , ϕ ( 0 ) = 0 , using Laplace transform.

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Answer 1

Question

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

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Answer 2

Question

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

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Answer 3

Question

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

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Answer 4

Question

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

Expert Solution & Answer

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Answer 5

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

(b)

To determine

To convert: The integral equation into an initial value problem.

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

Answer 6

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

Answer 7

Chapter 6.6, Problem 20P

(a)

To determine

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

Answer 8

(b)

To determine

To convert: The integral equation into an initial value problem.

Answer 9

(b)

To determine

To convert: The integral equation into an initial value problem.

Answer 10

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

Answer 11

(c)

To determine

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

Answer 12

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Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 6.1 - Prob. 1P Ch. 6.1 - Prob. 2P Ch. 6.1 - Prob. 3P Ch. 6.1 - Prob. 4P Ch. 6.1 - Prob. 5P Ch. 6.1 - Prob. 6P Ch. 6.1 - Prob. 7P Ch. 6.1 - Prob. 8P Ch. 6.1 - Prob. 9P Ch. 6.1 - Prob. 10P

The solution of the Integro - differential equation ϕ ′ ( t ) + ∫ 0 t ( t − ξ ) ϕ ( ξ ) d ξ = t , ϕ ( 0 ) = 0 , using Laplace transform.

The solution of the Integro - differential equation ϕ′(t)+∫0t(t−ξ)ϕ(ξ)dξ=t,ϕ(0)=0, using Laplace transform.

To convert: The integral equation into an initial value problem.

To solve: The initial value problem in the sub part (b) and to check whether the obtained solution is same as the one obtained in sub part (a).

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Chapter 6 Solutions