b)[ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution Short list of important Laplace transforms.f(t)F(s)| f(t)F(s)t" (integer n >0)cos ktI (s > 0)(s > 0)(s > 0)(s > a)(s > 0)eatsin ktu(t – a)Sa(t) = 8(t – a) (a > 0)eat cos ktf(m) (t)eat f(t)eat sin kts" F(s) – E=1 s"-k f(k=1)(0)F(s - a)e-as(8 > a)Só S(7) drf(at) (a > 0) F(s/a)k(8-a)2+k2F(s)8-a(s > a)(8-a)2+k2n!(8-a)n+IF(s)-as F(s)eat n (integern20)(8 > a)tf(t)u(t – a)f(t – a)ex" +5x'+6x = 5(t – 4), x(0) = 20, x'(0) = 7Solve the above IVP using Laplace Transforms and then find x(4.5).Put x(4.5) accurately calculated to the nearest thousandth (3 decimal places) in the answer box.Notation:d?xdx-and x x(t).dtx" =and x' =S(t) is the Dirac delta function.

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Answered: Short list of important Laplace…

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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[ordinary differential equations; topic] Please solve the following problem Provide a well explained and understandable(readable) Step by step solution solution

Short list of important Laplace transforms.
f(t)
F(s)
| f(t)
F(s)
t" (integer n >0)
cos kt
I (s > 0)
(s > 0)
(s > 0)
(s > a)
(s > 0)
eat
sin kt
u(t – a)
Sa(t) = 8(t – a) (a > 0)
eat cos kt
f(m) (t)
eat f(t)
eat sin kt
s" F(s) – E=1 s"-k f(k=1)(0)
F(s - a)
e-as
(8 > a)
Só S(7) dr
f(at) (a > 0) F(s/a)
k
(8-a)2+k2
F(s)
8-a
(s > a)
(8-a)2+k2
n!
(8-a)n+I
F(s)
-as F(s)
eat n (integern20)
(8 > a)
tf(t)
u(t – a)f(t – a)
e
x" +5x'+6x = 5(t – 4), x(0) = 20, x'(0) = 7
Solve the above IVP using Laplace Transforms and then find x(4.5).
Put x(4.5) accurately calculated to the nearest thousandth (3 decimal places) in the answer box.
Notation:
d?x
dx
-and x x(t).
dt
x" =
and x' =
S(t) is the Dirac delta function.

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