Solve the following ODE: x" + x = e-t with initial conditions x(0) = x'(0) = 0. Along the way, (1) Identify the transfer function H(s), and (ii) Use convolution instead of partial fractions to take the inverse Laplace transform.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Solve the following ODE: æ" + x = e_2t with initial conditions x(0) = x'(0) = 0. Along the way,
(i) Identify the transfer function H(s), and
(ii) Use convolution instead of partial fractions to take the inverse Laplace transform.
Transcribed Image Text:Solve the following ODE: æ" + x = e_2t with initial conditions x(0) = x'(0) = 0. Along the way, (i) Identify the transfer function H(s), and (ii) Use convolution instead of partial fractions to take the inverse Laplace transform.
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