a. Let g be the piecewise linear function 0, g(t)=(t-5), 1. t = [0,5) t≤ [5, 10) t> 10. Express g using step functions and find its Laplace transform. b. Solve the ODE y" + 4y = g(t), y(0) = 0, y'(0) = 0.
a. Let g be the piecewise linear function 0, g(t)=(t-5), 1. t = [0,5) t≤ [5, 10) t> 10. Express g using step functions and find its Laplace transform. b. Solve the ODE y" + 4y = g(t), y(0) = 0, y'(0) = 0.
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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ODE question，please use clear han dw r
Transcribed Image Text:a. Let g be the piecewise linear function
g(t)
=
0,
(t-5),
y" + 4y = g(t),
t = [0,5)
te [5, 10)
t > 10.
1,
Express g using step functions and find its Laplace transform.
b. Solve the ODE
y(0) = 0, y'(0) = 0.
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