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Given the differential equation - == y'' + 4y = 3et, y(0) = 0, y'(0) = 0 a) Apply the Laplace Transform and solve for Y(s) 3 Y(s): = (8-6)(s²+4) 3 (s - 6) (s² + 4) b) Now solve the IVP by using the inverse Laplace Transform y(t) = L−¹{Y(s)} 9 y(t) 3 6t 3 = 40 8 cos (2t) + sin(2t) x 20

Given the differential equation - == y'' + 4y = 3et, y(0) = 0, y'(0) = 0 a) Apply the Laplace Transform and solve for Y(s) 3 Y(s): = (8-6)(s²+4) 3 (s - 6) (s² + 4) b) Now solve the IVP by using the inverse Laplace Transform y(t) = L−¹{Y(s)} 9 y(t) 3 6t 3 = 40 8 cos (2t) + sin(2t) x 20

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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Given the differential equation - == y'' + 4y = 3et, y(0) = 0, y'(0) = 0 a) Apply the Laplace Transform and solve for Y(s) 3 Y(s): = (8-6)(s²+4) 3 (s - 6) (s² + 4) b) Now solve the IVP by using the inverse Laplace Transform y(t) = L−¹{Y(s)} 9 y(t) 3 6t 3 = 40 8 cos (2t) + sin(2t) x 20
Transcribed Image Text:Given the differential equation - == y'' + 4y = 3et, y(0) = 0, y'(0) = 0 a) Apply the Laplace Transform and solve for Y(s) 3 Y(s): = (8-6)(s²+4) 3 (s - 6) (s² + 4) b) Now solve the IVP by using the inverse Laplace Transform y(t) = L−¹{Y(s)} 9 y(t) 3 6t 3 = 40 8 cos (2t) + sin(2t) x 20
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