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11.
n
- tartibli chiziqli o‘zgarmas koeffitsientli differensial tenglamalar
1.
2
1
2
x
x
y
c e
c e
.
2.
2
1
2
x
x
y
c e
c e
.
3.
2
1
2
cos
sin
x
x
y
c e
x
c e
x
.
298
4.
2
2
1
2
cos3
sin3
x
x
y
c e
x
c e
x
.
5.
1
2
x
x
y
c e
c xe
.
6.
2
1
2
3
x
x
x
y
c e
c e
c e
.
7.
3
1
2
3
cos
sin
x
x
x
y
c e
c e
x
c e
x
.
8.
3
2
2
1
2
3
x
x
x
y
c e
c e
c xe
.
9.
1
2
3
4
cos 2
sin2
cos 2
sin2
y
c
x
c
x
c x
x
c x
x
.
10.
2
2
1
2
3
4
cos3
sin3
x
x
x
x
y
c e
c xe
c e
x
c e
x
.
11.
3
2
1
2
2
/
x
x
x
y
c e
c e
x e
.
12.
2
3
2
2
1
2
(
3
9)
x
x
x
y
y
c e
c e
x x
x
e
.
13.
2
2
3
2
3 2
1
2
2
6
9
6
x
x
x
y
c e
c xe
x
x
x
x e
.
14.
3
2
2
2
1
2
cos
7sin
1
5
10
x
x
x
x
x
x
y
c e
c e
xe
e
.
15.
1
2
3
cos
sin
x
y
c
c x
c e
x
x
.
16.
1
2
3
cos
sin
(
2)(cos
1) (
1)sin
x
y
c
x c
x c e
x
x
x
x
17.
1
2
3
sin
x
x
x
x
y
c e
c e
c xe
e
x
.
18.
1
2
3
cos
sin
2
4 (1
)
cos
(2
)
sin
x
x
x
x
x
y
c e
c e
x
c e
x
x
x e
x
x e
x
.
19.
y
1
2
3
4
cos
sin
3cos
sin
y
c
c x
c
x
c
x
x
x
x
.
20.
2
1
2
3
4
5
x
x
x
x
y
c e
c xe
c e
c xe
x
x
.
21.
2
cos
cos
2sin
sin
y
x
x
x
x
x
x
.
22.
2
2
3 3
x
x
x
y
x
e
xe
e
.
23.
2
2
5
5 4
x
y
x
x
e
.
24.
/2
/2
3
3
3
cos
3
sin
3
2
2
2
x
x
x
x
y
e
x
e
x
xe
e
.
12. Chegaraviy masalalar
1.
2
2
2
2
1
1
1
x
x
x
e
y
e
e
xe
e
e
.
2.
2
2
2
2
2
4
3
2
1
1
x
e
y
e
x
x
e
e
.
3.
cos
sin
(cos
sin ) 2
/
y
x
x
x
x
x
.
4.
cos
sin
2
x
x
x
.
5.
(
1)
2 ln
e e
y
x
x
x
x
.
6.
sin cos(1
), 0
,
1
( , )
cos(1
)sin ,
1.
cos1
x
x
G x
x
x
7.
1
, 0
,
( , )
(
1),
1.
x
x
e
x
G x
e e
x
8.
1
2
2
1
( )
( ), 0
,
1
( , )
( ) ( ),
1,
( )
y x y
x
G x
y x y
x
W
2
2
1
2
( )
2(cos
cos1 sin
sin1),
( )
cos
sin ,
( )
(cos1 sin1)cos
(cos1 sin1)sin .
W
y x
x
x
y x
x
x
9.
ln
(ln
ln 2), 0
,
1
( , )
(ln
ln 2) ln ,
1.
ln 2
x
x
G x
x
x
10.
arctg , 0
,
( , )
arctg ,
1.
x
x
G x
x
13. Differensial tenglamalarning normal sistemasi
1.
1
2
1
2
3
3
2
,
2
t
t
x
c
c e
y
c
c e
.
2.
1
2
1
2
2
3
3
(
)
,
(2
2
)
t
t
x
c
c t e
y
c
c
c t e
.
3.
2
1
2
1
2
1
1
1
sin ,
cos
0
2
2
t
t
t
t
x
c e
c e
t y
c e
c e
t
t
.
299
4.
2
2
1
1
2
2
1
2
1 2
2
4
,
4
2
2t
t
t
t
c
c
x
c
c e
e
t y
c
c e
c c e
.
5.
1
2
3
1
2
3
cos
sin ,
sin
cos ,
t
t
t
t
x
c
c e
t
c e
t y
c
c e
t
c e
t
1
2
3
sin
cos
t
t
z
c
c e
t
c e
t
.
6.
2
3
2
2
3
1
2
,
,
t
x
c t
c y
c t
c
c z
c e
c
.
10.
2
2
xy t
c
.
11.
x
y
z
c
.
12.
3
3
2
2
1
2
, 2(
) 3
6
y
c z
x
y
x y
x
c
.
13.
1
1
1
2
1
2
1
(
2
) ,
(
2
)
x
c c
c t
y
c
c t
.
14.
1
1
1
1
1
1
2
1
2
(
1)
(
1)
1
1
,
(
1)
1
(
1)
1
c
t
c
t
c
c
x
y
c
c
c e
c
c e
.
15.
1
2
1
2
1,
1
t
t
t
t
x
c e
c e
y
c e
c e
.
16.
2 2
2 2
1
2
3
2
3
3
2
,
,
t
t
t
t
t
t
x
c e
c te
c e
y
c e
c e
z
c e
.
17.
1
3
2
1
2
2
2
1
,
,
(
)(
ln
1)
c
c
x
y
z
c
t
c
c
t
c
t
c
t
.
18.
2
1 3
2
1 2
3
2
1 3
2
1 2
3
2
(
)
1
,
,
(
)(
2
)
c c c
c
c c t
x
y
c
c t c c
c
c c t
c
c t
2
2
3
2
1 3
2
1 2
.
(
)(
2
)
c
z
c
c t c c
c
c c t
14. Normal ko‘rinishdagi chiziqli differensial tenglamalar sistemasi
1.
Har qanday oraliqda chiziqli erkli.
2.
Har qanday oraliqda chiziqli boʻgʻliq.
3.
Har qanday oraliqda chiziqli erkli.
4.
Har qanday oraliqda chiziqli erkli.
5.
Har qanday oraliqda chiziqli boʻgʻliq.
6.
1
1
2
2
1
0
0
1
/
/
x
x
t
x
x
t
.
7.
1
1
2
2
1 (
1)
(1
)
0
1
/
/
t
x
x
t
e
t
x
x
.
8.
1
1
2
2
1
cos
sin
2sin
cos
sin
cos
cos
t
t
t
x
x
t
t
t
t
x
t
t
t
x
.
9.
1
2
3
2
2
1
2
3
3
1
2
3
3/2
1/2
1/2
1/2
1/2
1/2
1
1
,
(
1)
(1
)
1
4
3
2
1
1
,
1
2 (1
) 1
(1
)
1
2
.
1
2
1
2(
)
(
)
2(
)
(
)
dx
x
x
dt
t t
t
t
dx
t
t
t
x
x
x
dt
t
t
t
t
t
t
dx
t
x
x
x
dt
t
t
t
10.
1
2
2
2
,
3
1
t
t
t
x
c e
c e
t y
c e
t
.
11
.
1
2
2
2
2
(
)
2
1,
t
t
t
t
x
c e
te
c e
e
t
1
2
2
2
t
t
t
y
c te
c e
e
t
. Mos bir jinsli sistemani yoʻqotish usuli yordamida
yeching.
12.
1
2
2
1
(
) cos
(
)sin
ln cos
cos
ln cos
sin ,
x
c
c
t
c
c
t
t
t
t
t
t
t
1
2
cos
sin
sin
ln cos
cos
y
c
t
c
t
t
t
t
t
.
13.
2
1
2
(2ln
3),
x
c t
c
t
t
2
1
1
2
(3 2ln )
4 (ln
1)
y
c t
c
c
t
t
t
t
.
14.
2
1
2
1
2
(
3ln
3) 1,
(3
2
6ln
8)
x
t c t
c
t
y
t c t
c
t
.
300
15.
1
2
1
2
3
,
2
2
/
/
x
c t
c
t x
c t
c
t
. Mos bir jinsli sistemada
(
)
t
e
t
e
almashtirish bajaring.
16.
1
2
3
3
2
5
8
,
t
t
t
t
x
c e
c e
c e
e
2
3
3
2
2
2
,
t
t
t
y
c e
c e
e
2
3
3
2
2
2
2
t
t
t
z
c e
c e
e
.
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