①
'
Xy t 7
XYZ gli ) 7 day + PLX ) Q CX ) yn
=
y
= =
y
-
DX
'
y tyg
=
725
du
-
t ( I -
n )P (x )u = ( I -
n ) QLX)
a) Pix ) =L DX
X
Q (x ) =
7
n
= 2
' 2 '
b)
- -
=
u
y
=
y
' -
' '
u
y
=
y
-
off f f)
+ -
u =
-
7
""" " es #
" in
×=
¥
-
c) suit ) = e = =
e
uh ) f- HI
-
- '
=
7 In X t C
-
I
u x ) I
-
u
y
= =
ylx)
initial conditions :
X =
I
Ll ) 7
y
= -
Uli ) =
I =L
ya ) -
7
d) (x ) -7×1 nx
LyX
u
-
=
) y
'
(x )
-
-7×1 nx
IX
e = -
IX )
'
=/
Lx )
-
Tx in
y
-
x -
,②
¥y=y,÷ yet
de
-
-
I
dx
'
I #its
-
ya
①
3- -3=1×3
- " -
y dye y
-
DX
(
-
3
let u
y
=
-39¥ 54ft
-
-
"
EEF Fu Fs
- - -
-
,
II I Is
+ " = -
I.f .
=
ef¥d× =
×
6
uxb
f
'
DX
¥-3
= - .
X
=
f -
3×3 DX
= -
3×4 t C
4-
3
know that
-
u=y
3×6=-242×4 t C
-
y
initial
ya )
condition
= I
1 = -
I t C
4
I = C
4
'
13
⇐xii]
" "
'
, ③ 2yy
'
t 2 =
y
't 2x
y 101=6
'
Zyy
'
2x 2
y
-
= -
I
'
x I
yy
-
= -
2
'd
a) u =
y
un
y
-
-
I
'
-
y
2M
b) UM
'
u X I
21
=
. - -
÷ uz
x l
-
-
-_
'
U -
U
=
2X -
2
fp DX f -
DX - X
c) µc×)=e =
e =
e
=/
× ×
2)
-
-
e ulx ) e ( 2x -
DX
×
( ×dx
-
2)
-
= -
e ( 2x -
+ 2e
× ×
( 2x
- -
= -
e -
2) -
2e t C
×
U (X ) = -
( 2x -
2 ) -
2 + Ce
×
= -
2x tee
know that u=y2 and lo ) 6
-
y
-
2 ×
2x tee
y
= -
°
62 = -
210 ) t Ce
36 =
C
'
2x -136 ex
y
= -
't
=
l 2x -136 ex )
y
-
'
Xy t 7
XYZ gli ) 7 day + PLX ) Q CX ) yn
=
y
= =
y
-
DX
'
y tyg
=
725
du
-
t ( I -
n )P (x )u = ( I -
n ) QLX)
a) Pix ) =L DX
X
Q (x ) =
7
n
= 2
' 2 '
b)
- -
=
u
y
=
y
' -
' '
u
y
=
y
-
off f f)
+ -
u =
-
7
""" " es #
" in
×=
¥
-
c) suit ) = e = =
e
uh ) f- HI
-
- '
=
7 In X t C
-
I
u x ) I
-
u
y
= =
ylx)
initial conditions :
X =
I
Ll ) 7
y
= -
Uli ) =
I =L
ya ) -
7
d) (x ) -7×1 nx
LyX
u
-
=
) y
'
(x )
-
-7×1 nx
IX
e = -
IX )
'
=/
Lx )
-
Tx in
y
-
x -
,②
¥y=y,÷ yet
de
-
-
I
dx
'
I #its
-
ya
①
3- -3=1×3
- " -
y dye y
-
DX
(
-
3
let u
y
=
-39¥ 54ft
-
-
"
EEF Fu Fs
- - -
-
,
II I Is
+ " = -
I.f .
=
ef¥d× =
×
6
uxb
f
'
DX
¥-3
= - .
X
=
f -
3×3 DX
= -
3×4 t C
4-
3
know that
-
u=y
3×6=-242×4 t C
-
y
initial
ya )
condition
= I
1 = -
I t C
4
I = C
4
'
13
⇐xii]
" "
'
, ③ 2yy
'
t 2 =
y
't 2x
y 101=6
'
Zyy
'
2x 2
y
-
= -
I
'
x I
yy
-
= -
2
'd
a) u =
y
un
y
-
-
I
'
-
y
2M
b) UM
'
u X I
21
=
. - -
÷ uz
x l
-
-
-_
'
U -
U
=
2X -
2
fp DX f -
DX - X
c) µc×)=e =
e =
e
=/
× ×
2)
-
-
e ulx ) e ( 2x -
DX
×
( ×dx
-
2)
-
= -
e ( 2x -
+ 2e
× ×
( 2x
- -
= -
e -
2) -
2e t C
×
U (X ) = -
( 2x -
2 ) -
2 + Ce
×
= -
2x tee
know that u=y2 and lo ) 6
-
y
-
2 ×
2x tee
y
= -
°
62 = -
210 ) t Ce
36 =
C
'
2x -136 ex
y
= -
't
=
l 2x -136 ex )
y
-
