2 오
.
lI
iY ' t y
P (t 3
⇒
ta
=
µ (←
costa
=
el
=
)
=
비로
Y
=
Since
y (a 3
Hence
y
ty← ( t
p <t 3
=
Thea
+
) y
1 +
⇒
tay
"
ekee
ee
'
t
t
정
+
=
'
et (t + ) y
+
←
=
1
1 tae
,
'
=
-
e
st
-
1]
Coet
1+
=
1
tet
+
C
tFo
lnaee
( C . constant )
( C . :Constant
'
lnd
t
t
=
tet
=
←
tety
-
-
←
( tety )
tee
+
Since yCluz)
y
' 된 ' = 1
y
te
=
tety
⇒
Hence
constamt )
t
u (e ) =
=
.
, Co = ☆
=
t 30 ) "
⇒
y
(C
C
txo
(
Givem equatians
:
+
π
, O
.
t
sint
=
:
D
=
cost
=
( Eo Constant 3
tvsint
=
2ty = cost
s
tay )
(
tr
=
'
⇒
+
=
te
2 ay
t
tasint
=
eant
Glivenequartion
:
cost
q (t )
.
' o
: G. =
μ
Σ
2 2
.
# 5
e
dxdy
(y
-
+
dy
yβ+e ☆
separable
s
"
y
ay )
⇒
ㄹ
비7
feyx
=
-
( x
=
=
e
-
x'
+
e
ψ
-
, dx
☆
Hance
e
yx + 2 (ey - )
y
*
업
1 + 3×
=
β
-
( 3y
=
C
ytey to
with
separable
3
=
6y
C
←
'
by ] dy = [ ( + 3 ) dx
β-
y
⇒
x
-
y
3
?
since
y( 3 =
A(so
3 =6
.
x
=
β
,
o
y g
1
1
-
=
3
3y < y 23 # 0
=
( Co : Comstamt ]
C.
+ x +
Eo
,
y
β
β
'
-
3y
x
-
x
-
=
-
2
-
on
x- ) ( x + x + a 3=
(
2
y
Hence
=
y =ω x β+x - =
than
-
..
2 ☆ xβ+ x + 2 = ( x + 9 ) [x
=
=
0
x
∴
=의
x + a) = 0
∴ x =-
wity
w (o ) = w
1 ExE l
-
23
tw
‰
# 19 cas
By Newton
Them
'
second law
s
na
,
deda
=
⇒
m
s
tdntkv
=
-
mg
-
)
efde
eht
=
=
o
Since
x (t3
x(0 )
Then
☆√
Hence
x
,
dtdx
w =
Hence
⇒
.
=
(
eke- v ]
xm
k
+
[
t
+
=
G
.
=
w. +
+
+
O
ekt
(. + )
=
k
=
(
g
.
.
1 C
[v. + k>
제
with
ekt
[C
x ( 0) =δ
대울 재
=
.
( o : Constant )
율
.
:
Constant )
+
k
Xm =
-
gkr
houlltngkro ) knv
+
chamges from ( ) to ( >
←
=
:
0
+
-
fan = ebu ( 1
tm 재 + uJemkt m nvk 개
k
-
Ge
- +
-
v=
a
get
∴
,
whent I
업
.
=
tkw
dtx k
저 emkt
tC
여념 - 개 gk ]
is amars imacan
=-
-
'
. v
e
+ Co
= mk ) +
재
=
N. =
.
[
ddwy
=
W
'
i.
fon hieghe x
=
kew- mg
IVB
.
ekto =- tfCo
Since √ ( ) =√
⑪m
ama
ta
.e
'
=
ku
i
g
s ekt ☆ tetr
s
#
mg -k
s -
Thean . ( t
-
도F
.
+
+
kvmg )
: xm =
-
nklunkltmgkv . 재
)
+
.
4
# 3 ( 4 tryy
'
+
-
P
( t) =
Than
tay
3t
=
4 t
=
-
q
.
and
pley
ㆍ
(t) =
fle)
# 2o
4
-
is
=
Than ψ(t )
y ( 33 =
,
-
(
-
∞
-
(
on
1
-
-
3
∞ - 2)
ECr 6
-
,
,
(
-
2
,
23
.
2)
27
fon some CEIR
C φit)
=
tr
continuos
solationexistson
Let y(e)
( &(ts
Since y qcey
is
=
Tben
st
are
Sinceimitial condition
Hence
linean
⇒
다
러
for ψ(t )
solution
φ (t ) p (t) &(t )
'
,
+
'
,
ψ (t) + p(t3 ψ(←)
=
0
& it) p (t) Cφ(t)
=
(
=
C( φits + p( t 3φ(t)
Hernce Yce)= CScesis also a solur twon
-
+
=
CO
=
0
(2
,
∞ ]