Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Please do A and C
ot f(t) on [0, 0). action x(t) 6, 6et-3, 0≤t <3, 3<t<4, 4≤t<6, t≥ 6, 0, and find the Laplace tranform X (s). 6. Solve the following initial value problems using Laplace transforms. a) x² + 5x = H (t− 2), x(0) = 1. b) x² + x = sin 2t, x(0) = 0. c) x" - x² - 6x = 0, d) x" - 2x² + 2x = 0, e) x" - 2x² + 2x = et, f) x" - x' =0, x(0) = 1, x'(0) = 0. g) x" +0.4x' + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0. h) x" + 9x = sin 3t, x(0) = 0, x'(0) = 0. i) x" -2x = 1, x(0) = 1, x'(0) = 0. j) x' = 2x + H(t-1), x(0) = 0. 7. Sketch the function f(t) = 2H(t - 3) - 2H(t - 4) and find its La transform. x(0) = 2, x'(0) = -1 x(0) = 0, x'(0) = 1. x(0)=0, x'(0) = 1. 8. Find the Laplace transform of f(t) = t²H(t-3). 9. Invert F(s) = (-2)4 10. Find the inverse transform of F(s) 1-e-48
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Transcribed Image Text:ot f(t) on [0, 0). action x(t) 6, 6et-3, 0≤t <3, 3<t<4, 4≤t<6, t≥ 6, 0, and find the Laplace tranform X (s). 6. Solve the following initial value problems using Laplace transforms. a) x² + 5x = H (t− 2), x(0) = 1. b) x² + x = sin 2t, x(0) = 0. c) x" - x² - 6x = 0, d) x" - 2x² + 2x = 0, e) x" - 2x² + 2x = et, f) x" - x' =0, x(0) = 1, x'(0) = 0. g) x" +0.4x' + 2x = 1 - H(t-5), x(0)=0, x'(0) = 0. h) x" + 9x = sin 3t, x(0) = 0, x'(0) = 0. i) x" -2x = 1, x(0) = 1, x'(0) = 0. j) x' = 2x + H(t-1), x(0) = 0. 7. Sketch the function f(t) = 2H(t - 3) - 2H(t - 4) and find its La transform. x(0) = 2, x'(0) = -1 x(0) = 0, x'(0) = 1. x(0)=0, x'(0) = 1. 8. Find the Laplace transform of f(t) = t²H(t-3). 9. Invert F(s) = (-2)4 10. Find the inverse transform of F(s) 1-e-48
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