Which method is more correct?
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
100%
Which method is more correct?
![Given
y'+y = 5(t -R) cast
y (0) =0 , y10)= |
%3D
Taking
Laplace Tansform on both sides, ue get
%3D
using
[s+1] L{y} -I
y (o) =0
, y'co) = )
= L& sCt--m)cast} O
LĄ 8ct-am) cast}
of Laplace transform.
Now find
by wing defnitim
ue get
put
f(t) = 8it- pTT) cast
Lļ Sct-2m) cast} =S Et sit-eT) cost dt
we
can wnle ēstsrt- ) cartat
as
( SCE -2T) U(4) ēst cart at
where
u(t)
%3D
t7,0
using the formula
, ve get
st
( dt -aT) UCt) ecost dt =
os (25)
cost
Нелсе,
equation o becomer,
(S+) Lhyy -I
L{y(t)] =
%3D
Taking Laplace inverse
both sides, ue get
on
yie) = t') + }
RITS
e
using
]
a
y Ct) =
sint + Um(t) sinlt-<T)
%3D
which is required solutim of given inihal value
problem .](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe02838e7-dc45-4607-88b3-6692c936110a%2F6d5e31ca-d59c-47f7-b638-bf5e462aea74%2Fllci2lk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given
y'+y = 5(t -R) cast
y (0) =0 , y10)= |
%3D
Taking
Laplace Tansform on both sides, ue get
%3D
using
[s+1] L{y} -I
y (o) =0
, y'co) = )
= L& sCt--m)cast} O
LĄ 8ct-am) cast}
of Laplace transform.
Now find
by wing defnitim
ue get
put
f(t) = 8it- pTT) cast
Lļ Sct-2m) cast} =S Et sit-eT) cost dt
we
can wnle ēstsrt- ) cartat
as
( SCE -2T) U(4) ēst cart at
where
u(t)
%3D
t7,0
using the formula
, ve get
st
( dt -aT) UCt) ecost dt =
os (25)
cost
Нелсе,
equation o becomer,
(S+) Lhyy -I
L{y(t)] =
%3D
Taking Laplace inverse
both sides, ue get
on
yie) = t') + }
RITS
e
using
]
a
y Ct) =
sint + Um(t) sinlt-<T)
%3D
which is required solutim of given inihal value
problem .
![y"+y= S(t-28) cast , yloj= 0, L'10) =1
Taking oplace transfom on bath sides;
L[ y"ty]= L[S(t- 2x) Cost)
2
> se YCS)-sy l0)- y'lo)+ Y(S) = é"
Cos 2 t
(*: L[ fH) ult-a)] = é ? f(a))
as
(s*+) Y(5) - Sx0 -) ニ
2
it.
(6+1) YIS) = e
275
(: Ca82=1)
Taking beth sides;
in verse laplace on
e
こ
y(t) =
ft) Ult-27) + sint
cshene f(t)=
sin (t2T), t> 2
tく 2オ
And ult-27) s on voit step function
sint. Ult -27) +
y (t) = sint.Ult-27)+ Sint](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe02838e7-dc45-4607-88b3-6692c936110a%2F6d5e31ca-d59c-47f7-b638-bf5e462aea74%2F5ojsob_processed.jpeg&w=3840&q=75)
Transcribed Image Text:y"+y= S(t-28) cast , yloj= 0, L'10) =1
Taking oplace transfom on bath sides;
L[ y"ty]= L[S(t- 2x) Cost)
2
> se YCS)-sy l0)- y'lo)+ Y(S) = é"
Cos 2 t
(*: L[ fH) ult-a)] = é ? f(a))
as
(s*+) Y(5) - Sx0 -) ニ
2
it.
(6+1) YIS) = e
275
(: Ca82=1)
Taking beth sides;
in verse laplace on
e
こ
y(t) =
ft) Ult-27) + sint
cshene f(t)=
sin (t2T), t> 2
tく 2オ
And ult-27) s on voit step function
sint. Ult -27) +
y (t) = sint.Ult-27)+ Sint
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