Program Explanation Given information: The differential equation is written as, x ″ + 9 x = δ ( t − 3 π ) + cos 3 t The initial values for differential equation is written as, x ( 0 ) = 0 x ′ ( 0 ) = 0 Calculation: Take the Laplace transform of the given differential equation and solve as shown below. x ″ + 9 x = δ ( t − 3 π ) + cos 3 t L { x ″ ( t ) + 9 x ( t ) } = L { δ ( t − 3 π ) + cos 3 t } L { x ″ ( t ) } + 9 L { x ( t ) } = L { δ ( t − 3 π ) } + L { cos 3 t } Further, simplify the expression as, ( s 2 L { x ( t ) } − s x ( 0 ) − x ′ ( 0 ) ) + 9 L { x ( t ) } = ( e ( − 3 π ) s ) + s s 2 + 9 ( s 2 L { x ( t ) } − s ( 0 ) − ( 0 ) ) + 9 L { x ( t ) } = e − 3 π s + s s 2 + 9 s 2 L { x ( t ) } + 9 L { x ( t ) } = e − 3 π s + s s 2 + 9 ( s 2 + 9 ) L { x ( t ) } = e − 3 π s + s s 2 + 9 Further, simplify the expression as, L { x ( t ) } = e − 3 π s ( s 2 + 9 ) + s ( s 2 + 9 ) 2 x ( t ) = L − 1 { e − 3 π s ( s 2

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

5th Edition

ISBN: 9780134872971

Author: Edwards, C., Penney, David, Calvis

Publisher: PEARSON

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Chapter 7.6, Problem 6P

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Program Description: Purpose of the problem is to solve the initial value problem x″+9x=δ(t−3π)+cos3t;x(0)=x′(0)=0 and graph the solution.

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Chapter 7.6, Problem 5P

Chapter 7.6, Problem 7P

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Chapter 7 Solutions

MyLab Math with Pearson eText -- 24-Month Standalone Access Card -- For Differential Equations and Boundary Value Problems: Computing and Modeling Tech Update

Ch. 7.1 - Apply the definition in (1) to find directly tile...Ch. 7.1 - Prob. 2P Ch. 7.1 - Prob. 3P Ch. 7.1 - Prob. 4P Ch. 7.1 - Prob. 5P Ch. 7.1 - Prob. 6P Ch. 7.1 - Prob. 7P Ch. 7.1 - Prob. 8P Ch. 7.1 - Prob. 9P Ch. 7.1 - Prob. 10P

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Program Description: Purpose of the problem is to solve the initial value problem x ″ + 9 x = δ ( t − 3 π ) + cos 3 t ; x ( 0 ) = x ′ ( 0 ) = 0 and graph the solution.

Solution Summary: The author explains the purpose of the problem, which is to solve the initial value problem and graph the solution.

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Program Description: Purpose of the problem is to solve the initial value problem x″+9x=δ(t−3π)+cos3t;x(0)=x′(0)=0 and graph the solution.

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Chapter 7 Solutions