Explanation The given integral equation is y ( t ) = 1 − ∫ 0 t y ( τ ) t − τ d τ . Take Laplace transform on both sides and solve as follows. L { y ( t ) } = L { 1 − ∫ 0 t y ( τ ) t − τ d τ } Y ( s ) = L { 1 } − L { ∫ 0 t y ( τ ) t − τ d τ } Y ( s ) = 1 s − Y ( s ) π s Y ( s ) [ 1 + π s ] = 1 s Simplify further as follows

Differential Equations with Boundary-Value Problems

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ISBN: 9781337632515

Author: Dennis G. Zill

Publisher: Cengage Learning US

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Chapter 14.1, Problem 9E

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To solve: The integral equation y(t)=1−∫0ty(τ)t−τdτ.

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Chapter 14.1, Problem 8E

Chapter 14.1, Problem 10E

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Chapter 14 Solutions

Differential Equations with Boundary-Value Problems

Ch. 14.1 - (a) Show that erf(t)=10ted. (b) Use part (a), the...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Use the third and fifth entries in Table 14.1.1 to...

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The integral equation y ( t ) = 1 − ∫ 0 t y ( τ ) t − τ d τ .

Solution Summary: The author explains how to solve the integral equation y(t)=1-displaystyle int.

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To solve: The integral equation y(t)=1−∫0ty(τ)t−τdτ.

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Chapter 14 Solutions