3.12 Find the complete time-domain solutions for the follow- ing differential equations using Laplace transforms: dx(0) = 0, dt d³x (a) + 4x = e' with x(0) = 0, dt3 (b) (c) dx dt d²x dt² - 12x = sin 3t x(0) = 0 +6dx dt + 25x = et x(0) = 0, dx(0) dt d²x(0) dt² = 0 = 0
3.12 Find the complete time-domain solutions for the follow- ing differential equations using Laplace transforms: dx(0) = 0, dt d³x (a) + 4x = e' with x(0) = 0, dt3 (b) (c) dx dt d²x dt² - 12x = sin 3t x(0) = 0 +6dx dt + 25x = et x(0) = 0, dx(0) dt d²x(0) dt² = 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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Transcribed Image Text:3.12 Find the complete time-domain solutions for the follow-
ing differential equations using Laplace transforms:
dx(0)
dt
d³x
(a) + 4x = e' with x(0) = 0,
dt3
dx
dt
(b) - 12x = sin 3t x(0) = 0
-
(c)
d²x
dt²
+6dx
dt
+ 25x = e x(0) = 0,
= 0,
dx(0)
dt
d²x(0)
dt²
= 0
= 0
23 agil
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