Explanation It is given that the differential equation is y ′ ′ + 2 y ′ + 5 y = 10 cos t with the initial conditions y ( 0 ) = 2 and y ′ ( 0 ) = 1 . Apply Laplace transform on the function as follows. L ( y ′ ′ ) + L ( 2 y ′ ) + L ( 5 y ) = L ( 10 cos t ) L ( y ′ ′ ) + 2 L ( y ′ ) + 5 L ( y ) = 10 L ( cos t ) s 2 L ( y ) − s y ( 0 ) − y ′ ( 0 ) + 2 s L ( y ) − 2 y ( 0 ) + 5 L ( y ) = 10 s s 2 + 1 s 2 L ( y ) − 2 s − 1 + 2 s L ( y ) − 4 + 5 L ( y ) = 10 s s 2 + 1 On further simplification and applying inverse Laplace transform, ( s 2 + 2 s + 5 ) L ( y ) = 10 s s 2 + 1 + 2 s + 5 L ( y ) = 10 s ( s 2 + 1 ) ( s 2 + 2 s + 5 ) + 2 s + 5 s 2 + 2 s + 5 L ( y ) = 10 s ( s 2 + 1 ) ( ( s + 1 )

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

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ISBN: 9780137554843

Author: Allyn Washington, Richard Evans

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Chapter 31, Problem 54RE

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Chapter 31, Problem 53RE

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Chapter 31 Solutions

Pearson eText for Basic Technical Mathematics with Calculus -- Instant Access (Pearson+)

Ch. 31.1 - Show that is a solution of . Is it the general...Ch. 31.1 - Prob. 1E Ch. 31.1 - In Exercises 1 and 2, show that the indicated...Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 4E Ch. 31.1 - In Exercises 3–6, determine whether the given...Ch. 31.1 - Prob. 6E Ch. 31.1 - In Exercises 7–10, show that each function y =...Ch. 31.1 - Prob. 8E Ch. 31.1 - In Exercises 7–10, show that each function y =...

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