Sh. Merajova
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matematik fizika tenglamalaridan masalalar toplami
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19. . cos 1 n k k n t x e 20. . 4 1 4 1 | | 2 2 t x n e t
4 1 4 1 | | 2 2 2 t x n e t 22. . 4 1 sin 4 1 4 1 | | 1 2 2 t x nt n k k n e t x t 23. . 4 1 1 2 1 4 1 1
k k x n t e nt 5-bo‘lim 1. . 4 1 2 cos 1 2 ) 1 2 sin( 8 0 2 2 3 3 k t k k x k 2. . ) 1 2 sin( ) 1 2 sin(
) 1 2 cos( 1 2 1 8 0 3
t x k t k t k k e
3. . 2 ) 1 2 ( cos 2 ) 1 2 ( sin ) 1 2 ( 2 ) 1 ( 1 2 1 8 0 2 k k t x k t k k k e
4.
. 4 1
, sin
2 sin
1 cos
2 1 ) 1 ( 1 2 3 2 k k k k k t k kx t t k e x t
5. . 1 2
, 2 sin sin 4 ) 2 ( 1 2 3 3 2 k k k k k k kx t k k t x t
6. . 1 , sin sin 1 ) 1 ( 2 1 2 2 1 k k k k k k l k l kx t t k l xt
7. . sin
cos 1 2 ) 1 ( 2 cos
2 sin
1 3
k kx kt k t x 8. . 4 1 1 2
, 1 2 4
, ) 1 2 sin(
sin 1 cos 1 2 2 3 3 2 k k c x k t t e c k k k k k t k Ko‘rsatma. Yechimni 1 sin ) ( ) , ( k k x k t T t x u qator ko‘rinishida qidiring. Izoh. Yechimni v u
yig‘indi ko‘rinishida qidirish mumkin, bu yerda ) 1 ( 2 1
x v funksiya tenglamani va chegaraviy shartlarni qanoatlantiradi. U holda . )
2 sin(
sin 2 1 cos 2 ) 1 ( ) , ( 0 2 k t k k k x k e t t x x t x u
9. . cos
3 2 2 x te e e xt t t t 10. . sin 8 4 8 5 3 2 x t e e t t t x t t 11. . 2 3 cos
5 4 5 1 ) 1 ( 2 2 5 x e e t x t t
. 3
15 1 6 1 10 1 5 2
e e e xt x t t
13. . 3 cos 1 x e t e xt t t 14. . 2 cos 2 4 1 8 1 2 2 2
t e e t t
). 1
3 sin
) 1 3 ( sin
9 1
x t ch x 47
16. . sin
2 2
e e e xt x t t 17. l n n t l a n n dx l nx x u l a l nx e a 0 0 1 sin
) ( 2 yerda
bu
, sin 2
. 1 2 sin
1 2 1 4 ) , ( uchun
lgani
bo'
, ) ( 0 1 2 0 2 2 2 2
t l a k l x k e k A t x u const A x u 18. . 1 2 sin
1 2 1 8 ) , (
0 1 2 3 3 2 2 2 2 2
t l a k l x k e k Al t x u 19. 1 2 2 2 sin 1 2 2 2 2
n l t a n n n l x e a l n , bu yerda , sin
) ( 0 0 l n n dx l x x u a
,...) 2 , 1 (
,
n -
, 0
hl tenglamaning musbat ildizlari. 20. 1 2 , 2 sin
cos 2 2 2 2
n n n n l t a n l x l x e b l n bu yerda , sin cos ) ( 0 0
n n n n dx l x l x x u b
,...) 2 , 1 (
,
n - 2 1 ctg , 0
tenglamaning musbat ildizlari. 21. 0
. 22.
. 2 ) , ( , 1 2 cos
1 2 1 1 2 2 0 t 0 1 2 0 0 lim
2 2 2 2 u t x u l x k e k u u k l t a k k 23.
. 2 ) , (
, 1 2 2 cos
1 2 1 1 4 2 0 t 0 1 2 4 2 0 0 lim 2 2 2 2
t x u l x k e k u u k l t a k k 24.
. 2 1 2 cos
1 2 1 1 32 0 2 1 2 3 3 2
t n n x n e n 25.
. 1 2 sin
1 2 1 1 4 0 1 1 2 2 k t l k k l x k e k 26. . 1 2 sin
1 2 1 8 0 1 2 2 2
t k x k e k
. 2 1 2
; cos
1 2 8 0 2 2 2 l k x k e l l x k k k t k 28. . 3 cos 1 8 1 cos 8
e x t t 29. . sin 2 t t x e xt 30. . 3 sin 1 8 1 sin 8
e x t x t
31. . 2 cos 1 4 1 4 2
t e tx t Download 1.42 Mb. Do'stlaringiz bilan baham: 
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