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Question 32 Apply the Laplace transform method to resolve the subsequent initial value challenge: x"+2x=0, x(0) = -3, x(0) = 6. By employing X to denote the Laplace transform of x(t), expressed as X = L{x(t)}, determine the resultant equation from the application of the Laplace transform to the given differential equation. _=0 Using what you know, solve for X(s)=__ Present the solution in its partial fraction decomposition form as follows: X(s) = A/(sta) + B/(stb), ensuring that a < b. X(s)=_ Now, proceed to obtain the inverse transform to determine the expression for: x(t) =

Question 32 Apply the Laplace transform method to resolve the subsequent initial value challenge: x"+2x=0, x(0) = -3, x(0) = 6. By employing X to denote the Laplace transform of x(t), expressed as X = L{x(t)}, determine the resultant equation from the application of the Laplace transform to the given differential equation. _=0 Using what you know, solve for X(s)=__ Present the solution in its partial fraction decomposition form as follows: X(s) = A/(sta) + B/(stb), ensuring that a < b. X(s)=_ Now, proceed to obtain the inverse transform to determine the expression for: x(t) =

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter6: The Trigonometric Functions
Section6.6: Additional Trigonometric Graphs
Problem 77E
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Question 32 Apply the Laplace transform method to resolve the subsequent initial value challenge: x" +2x=0, x(0) = -3, x(0) = 6. By employing X to denote the Laplace transform of x(t), expressed as X = L{x(t)}, determine the resultant equation from the application of the Laplace transform to the given differential equation. =0 Using what you know, solve for X(s)=_ Present the solution in its partial fraction decomposition form as follows: X(s) = A/(sta) + B/(stb), ensuring that a < b. X(s)=_ Now, proceed to obtain the inverse transform to determine the expression for: x(t) =
Transcribed Image Text:Question 32 Apply the Laplace transform method to resolve the subsequent initial value challenge: x" +2x=0, x(0) = -3, x(0) = 6. By employing X to denote the Laplace transform of x(t), expressed as X = L{x(t)}, determine the resultant equation from the application of the Laplace transform to the given differential equation. =0 Using what you know, solve for X(s)=_ Present the solution in its partial fraction decomposition form as follows: X(s) = A/(sta) + B/(stb), ensuring that a < b. X(s)=_ Now, proceed to obtain the inverse transform to determine the expression for: x(t) =
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