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Consider the initial value problem where g(t) = ft 10 if 0

Consider the initial value problem where g(t) = ft 10 if 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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Consider the initial value problem where g(t) = ft 10 if 0 < t <3 if 3 < t < 0. y" + 4y = g(t), -3e^(-3s)/s-e^(-3s)/s^2+1/s^2 y(0) = 0, y'(0) = 0, a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). = (-3s-1)/s^2e^(-3s)+1/s^2 (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = -(3s+1)/s^2(s^2+3)e^(-3s)+1/(s^2(s^2+3)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 1/4(t-sin(2t)/2) help
Transcribed Image Text:Consider the initial value problem where g(t) = ft 10 if 0 < t <3 if 3 < t < 0. y" + 4y = g(t), -3e^(-3s)/s-e^(-3s)/s^2+1/s^2 y(0) = 0, y'(0) = 0, a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to the other (until you get to part (b) below). = (-3s-1)/s^2e^(-3s)+1/s^2 (formulas) b. Solve your equation for Y(s). Y(s) = L{y(t)} = -(3s+1)/s^2(s^2+3)e^(-3s)+1/(s^2(s^2+3)) c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). y(t) = 1/4(t-sin(2t)/2) help
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