№140 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
xx
yy
u
u
tenglamaning ( ,0)
( ),
( ,0)
0
y
u x
f x u
x
shartlarni qanoatlantiruvchi yechimini toping
2
u
f x y
f x y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
u
f x
f x y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
u
f x y
f y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
u
f x y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
№141 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
4
xx
yy
u
u
tenglamaning
( , 0)
( ),
( , 0)
0
y
u x
f x u
x
shartlarni qanoatlantiruvchi yechimini toping
2
2
4
u
f
x y
f
x y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
4
u
f
x
f y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
4
u
f x
f y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
2
2
4
u
f
x y
f x
y
bu yerda
2
( )
f
C I
bo’lgan ixtiyoriy funksiyalar
№142 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
9
0
xx
yy
u
u
tenglama umumiy yechimini ko’rsating?
)
3
(
)
3
(
)
,
(
x
y
g
x
y
f
y
x
u
( , )
(
)
(3
)
u x y
f y
x
g
y
x
( , )
(
3 )
(
3 )
u x y
f y
x
g y
x
)
(
)
3
(
)
,
(
x
y
g
x
y
f
y
x
u
№143 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
Berilgan to‘lqin tenglamasi uchun mos berilgan yechim to‘g‘ri holini belgilang.
2
1
0,
xx
tt
u
u
u
x
at
x
at
a
2
1
1
0,
xx
tt
a u
u
u
x
t
x
t
a
a
2
1
0,
xx
tt
u
u
u
x at
x at
a
2
0,
xx
tt
u
a u
u
x
at
x
at
№144 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
,
0
u x y
x
tenglamaning umumiy yechimi quyidagi hollarning qaysi birida to‘g‘ri ko‘rsatilgan.
,
u x y
f y
)
(
)
,
(
x
f
y
x
u
)
(
)
(
)
,
(
y
g
x
f
y
x
u
)
,
(
)
,
(
y
x
f
y
x
u
№145 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
Giperbolik tipdagi tenglamalar yechimi uchun qaysi hollardagi formulalar nomi to‘g‘ri.
Dalamber, Puasson, Kirxgof
Koshi, Puasson, Dirixle
Dalamber, Neyman, Koshi
Dirixle, Neyman, Dalamber
№146 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-3;
0
xy
u
tenglamaning umumiy yechimini toping.
)
(
)
(
y
g
x
f
)
,
(
y
x
f
)
( x
f
)
( y
g
№147 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
xx
u
tenglamaning umumiy yechimini toping.
)
(
)
(
y
g
y
f
x
)
,
(
y
x
f
)
( x
f
)
( y
g
№148 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
yy
u
tenglamaning umumiy yechimini toping.
)
(
)
(
x
g
x
f
y
)
(
)
(
y
g
y
f
x
)
(
)
(
y
g
x
f
)
( y
g
№149 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
Gursa masalasida shartlar qayerda qo’yiladi?
Xarakteristikada
0
t
da
0
x
da
l
x
da
№150 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-3;
y
x
u
u
tenglamaning umumiy yechimini ko’rsating
)
(
y
x
f
u
)
(
y
x
f
u
)
(xy
f
u
)
(
y
x
f
u
№151 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
y
x
u
u
tenglamaning umuniy yechimini ko’rsating
)
(
y
x
f
u
)
(
y
x
f
u
)
(xy
f
u
)
(
y
x
f
u
№152 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
y
x
yu
xu
tenglamaning umuniy yechimini ko’rsating
)
(xy
f
u
)
(
y
x
f
u
)
(
y
x
f
u
)
(
y
x
f
u
№153 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
0
y
x
yu
xu
tenglamaning umuniy yechimini ko’rsating
)
(
y
x
f
u
)
(
y
x
f
u
)
(xy
f
u
)
(
y
x
f
u
№154 Fan bobi-2; Fan bo`limi-1; Qiyinlik darajasi-2;
t
xx
u
u
u
tenglama uchun boshlang’ich shartni aniqlang?
,0
u x
x
,0
t
u x
x
,
u x
x
x
x
t
t
x
u
u
x
№155 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-1;
t
xx
u
u
tenglamaning
,0
sin
u x
x
shartni qanoatlantiruvchi yechimga qaysi javobda to’g’ri ko'rsatilgan
,
sin
t
u x t
e
x
,
cos 2
t
u x t
e
x
2
,
l t
u x t
e
tglx
,
cos sin
u x t
t
lx
.
№156 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
4
t
xx
u
u
tenglamaning
,0
cos 2
u x
x
shartni qanoatlantiruvchi yechimga qaysi javobda to‘g‘ri ko'rsatilgan
16
,
cos 2
t
u x t
e
x
4
cos 2
t
u
e
x
,
16
,
2
t
u x t
e
tg x
sin 2 cos 4
u
t
x
№157 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
9
t
xx
u
u
tenglamaning
,0
u x
chx
shartni qanoatlantiruvchi yechimini aniqlang
9
,
t
u x t
e chx
,
9
s 3
t
u
e
h x
,
3
,
sin 9
t
u x t
e
x
9
,
cos9
t
u x t
e
x
.
№158 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
t
xx
u
u
,
,0
2
u x
sh x
Koshi masalasi yechimini toping..
4
2
t
e
sh x
u
,
4
cos 2
t
u
e
x
,
2
2
t
e
ch
x
u
2
l t
u
e
tglx
№159 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
t
xx
u
u
,
,0
u x
shlx
Koshi masalasi yechimini toping..
2
l t
e
shlx
u
,
2
cos
l t
u
e
lx
,
2
l t
e
chlx
u
2
l t
u
e
tglx
№160 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
2
t
xx
u
a u
parabolik tenglama uchun boshlang’ich shartni aniqlang?
,0
u x
x
,0
t
u x
x
,
u x
x
x
x
t
t
x
u
u
x
№161 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
t
xx
u
u
tenglamaning
,0
sin
u x
lx
shartni qanoatlantiruvchi yechimga qaysi javobda to’g’ri ko'rsatilgan
2
,
sin
l t
u x t
e
lx
2
,
cos
l t
u x t
e
lx
2
,
l t
u x t
e
tglx
,
cos sin
u x t
t
lx
.
№162 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
t
xx
u
u
tenglamaning
,0
cos
u x
kx
shartni qanoatlantiruvchi yechimga qaysi javobda to’g’ri ko'rsatilgan
2
,
cos
k t
u x t
e
kx
2
cos
l t
u
e
kx
2
,
k t
u x t
e
tgkx
sin cos
u
lt
kx
№163 Fan bobi-3; Fan bo`limi-2; Qiyinlik darajasi-2;
t
xx
u
u
tenglamaning
,0
u x
chlx
shartni qanoatlantiruvchi yechimini aniqlang
2
,
l t
u x t
e
chlx
,
2
s
l t
u
e
hlx
,
2
,
sin
l t
u x t
e
lx
,
2
,
cos
l t
u x t
e
lx
.
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