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3. Use Laplace transforms to solve the following initial value problems: (a) 2y + y = 0, y(0) = -3 (b) y" - 4y = 6e³t - 3e-t, y(0) = 1, y'(0) = -1 (c) y - y = 2 cos(5t), y(0) = 0

3. Use Laplace transforms to solve the following initial value problems: (a) 2y + y = 0, y(0) = -3 (b) y" - 4y = 6e³t - 3e-t, y(0) = 1, y'(0) = -1 (c) y - y = 2 cos(5t), y(0) = 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem 3: Solving Initial Value Problems Using Laplace Transforms** Solve the following initial value problems using Laplace transforms: (a) \( 2y' + y = 0, \quad y(0) = -3 \) (b) \( y'' - 4y' = 6e^{3t} - 3e^{-t}, \quad y(0) = 1, \quad y'(0) = -1 \) (c) \( y' - y = 2\cos(5t), \quad y(0) = 0 \)
Transcribed Image Text:**Problem 3: Solving Initial Value Problems Using Laplace Transforms** Solve the following initial value problems using Laplace transforms: (a) \( 2y' + y = 0, \quad y(0) = -3 \) (b) \( y'' - 4y' = 6e^{3t} - 3e^{-t}, \quad y(0) = 1, \quad y'(0) = -1 \) (c) \( y' - y = 2\cos(5t), \quad y(0) = 0 \)
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