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b) Find constants a and b for which the inverse Laplace transform of s-1 F(s) = ²+2s+5 is f(t) = e¯¹ (a cos 2t + b sin 2t), t ≥ 0. c) Using the result in b) solve the differential equation:- d²y dt² dy when y(0) = 1 and (0) = -3. dt dy dt + 5y = 0,

b) Find constants a and b for which the inverse Laplace transform of s-1 F(s) = ²+2s+5 is f(t) = e¯¹ (a cos 2t + b sin 2t), t ≥ 0. c) Using the result in b) solve the differential equation:- d²y dt² dy when y(0) = 1 and (0) = -3. dt dy dt + 5y = 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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part B and C

a) Using the first shift theorem, when necessary (see below for a statement) write down the Laplace transforms of:- i. f₁(t) = -5e-³t, t≥ 0, ii. f₂(t) = e-³tt, t≥0, and hence find the Laplace transform of: g(t) = (2t - 5)e-3t, t≥ 0. b) Find constants a and b for which the inverse Laplace transform of S 1 s²+2s+5 F(s) = is f(t) = e-t (a cos 2t + b sin 2t), t ≥ 0. c) Using the result in b) solve the differential equation:- d²y dy +2 + 5y = 0, dt² dt when y(0) = 1 and (0) dy dt = -3.
Transcribed Image Text:a) Using the first shift theorem, when necessary (see below for a statement) write down the Laplace transforms of:- i. f₁(t) = -5e-³t, t≥ 0, ii. f₂(t) = e-³tt, t≥0, and hence find the Laplace transform of: g(t) = (2t - 5)e-3t, t≥ 0. b) Find constants a and b for which the inverse Laplace transform of S 1 s²+2s+5 F(s) = is f(t) = e-t (a cos 2t + b sin 2t), t ≥ 0. c) Using the result in b) solve the differential equation:- d²y dy +2 + 5y = 0, dt² dt when y(0) = 1 and (0) dy dt = -3.
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