x" +4x'+3x = 5(t – 4), x(0) = 4, x'(0) = 2 Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt and x' = dt? 5(t) is the Dirac delta function.
x" +4x'+3x = 5(t – 4), x(0) = 4, x'(0) = 2 Solve the above IVP using Laplace Transforms and then find x(4.2). Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box. Notation: dx -and x = x(t). dt and x' = dt? 5(t) is the Dirac delta function.
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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Question
4)
please solve the following
[ordinary
Transcribed Image Text:Short list of important Laplace transforms.
f(t)
F(s)
| f(t)
F(s)
(s > a)
(8 > 0)
s" F(s) – E-1 s"-k f(k-1) (0)
F(s – a)
n!
t" (integer n 2 0)
cos kt
(s > 0)
(s > 0)
(s > 0)
eat
8-a
sin kt
u(t – a)
da (t) = 6(t – a) (a > 0)
eat cos kt
f(n) (t)
eat f(t)
(8 > a) | eat sin kt
(n < s) Itu(D-s)
Só s(7) dr
e-as
k=1
eas
(s > a)
8-a
(メーa)2+2
n!
(sーa)2+2
F(s)
eat in (integer n > 0)
tf(t)
u(t – a)f(t – a)
F(s)
e-as F(s)
F(s/a)
f(at) (a > 0)
x" +4x'+3x S(t – 4), x(0) = 4, x'(0)
= 2
-
Solve the above IVP using Laplace Transforms and then find x(4.2).
Put x(4.2) accurately calculated to the nearest thousandth (3 decimal places) in the answer box.
Notation:
dx
-and x = x(t).
dt
dex
x":
and x' =
dt?
5(t) is the Dirac delta function.
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