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Consider the initial value problem y + 3y = 0 9 0 if 0 < t < 2 if 2 < t < 7 if 7 < t < ∞, y(0) = 4.

Consider the initial value problem y + 3y = 0 9 0 if 0 < t < 2 if 2 < t < 7 if 7 < t < ∞, y(0) = 4.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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Consider the initial value problem b. Solve your equation for Y(s). y + 3y 0 9 0 if 0 ≤ t < 2 if 2 < t < 7 if 7 < t < ∞, 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). y(t) = Y(s) = L {y(t)} = (9(e^(-2s)-e^(-7s))+4s)/(s(s+3)) y(0) = 4. (9(e^(-2s)-e^(-7s)))/s c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). help (formulas)
Transcribed Image Text:Consider the initial value problem b. Solve your equation for Y(s). y + 3y 0 9 0 if 0 ≤ t < 2 if 2 < t < 7 if 7 < t < ∞, 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). y(t) = Y(s) = L {y(t)} = (9(e^(-2s)-e^(-7s))+4s)/(s(s+3)) y(0) = 4. (9(e^(-2s)-e^(-7s)))/s c. Take the inverse Laplace transform of both sides of the previous equation to solve for y(t). help (formulas)
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