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4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) = 1.5. b) y" - y' - 6y = 0, y(0) = 11, y'(0) = 28 c) y" - 4y + 3y = 6t8, y(0) = 0, y′(0) = 0 d) y" + 3y' +2.25y = 9t³ +64, y(0) = 1, y'(0) = 31.5 e) y" + 3y' - 4y = 6e²t-3, y(1.5) = 4, y′(1.5) = 5

4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) = 1.5. b) y" - y' - 6y = 0, y(0) = 11, y'(0) = 28 c) y" - 4y + 3y = 6t8, y(0) = 0, y′(0) = 0 d) y" + 3y' +2.25y = 9t³ +64, y(0) = 1, y'(0) = 31.5 e) y" + 3y' - 4y = 6e²t-3, y(1.5) = 4, y′(1.5) = 5

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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Please use the Laplace transform. I only need help with part d

4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) = 1.5. b) y" — y' - 6y = 0, y(0) = 11, y'(0) = 28 - c) y" - 4y + 3y = 6t - 8, y(0) = 0, y′(0) = 0 d) y" + 3y' +2.25y = 9t³ +64, y(0) = 1, y′(0) = 31.5 e) y" + 3y' - 4y = 6e²t-3, y(1.5) = 4, y′(1.5) = 5
Transcribed Image Text:4. Solve the following initial value problems using the Laplace transform: a) y' + 3y = 0, y(0) = 1.5. b) y" — y' - 6y = 0, y(0) = 11, y'(0) = 28 - c) y" - 4y + 3y = 6t - 8, y(0) = 0, y′(0) = 0 d) y" + 3y' +2.25y = 9t³ +64, y(0) = 1, y′(0) = 31.5 e) y" + 3y' - 4y = 6e²t-3, y(1.5) = 4, y′(1.5) = 5
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