4)please solve the following[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)(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)eat8-asin ktu(t – a)da (t) = 6(t – a) (a > 0)eat cos ktf(n) (t)eat f(t)(8 > a) | eat sin kt(n < s) Itu(D-s)Só s(7) dre-ask=1eas(s > a)8-a(メーa)2+2n!(sーa)2+2F(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).dtdexx":and x' =dt?5(t) is the Dirac delta function.

The answer is given as follows:

Answered: x" +4x'+3x = 5(t – 4), x(0) = 4, x'(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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please solve the following

[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)
(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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