Differensial tenglamalar va ular bilan bog’liq tushunchalar
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1-kurs talabalari uchun Differensial tenglama fanidan ON va YaN uchun test savollari
- Bu sahifa navigatsiya:
- A) x x y 2 sin sin 3 .
- A) x e y 2 3 .
A) x x e C e C y 2 2 1 . B) x x e C e C y 2 1 . C) x x e C e C y 3 2 5 1 .
D) x e x C x C y ) sin cos ( 2 1 . E) 2 2
1 C e C y x . 31.
0 2 3
y y , y(0)=0, y′(0)=1 Koshi masalasi yechimini toping . A) x x y 2 sin sin 3 . B) 2 /
( x x e e y . C) x x e e y 2 . D) x x y cos
2 2 cos ; E) 2 / ) ( 2
x e e y .
32. 0 4 4
y y tenglamaning umumiy yechimini toping . A) x e C C y 2 2 1 . B) x e C x C y 2 2 1 ) ( . C) x e C x C y 2 2 1 ) ( . D) x C x C y 2 sin 2 cos
2 1 . E) x e x C x C y 2 2 1 ) cos sin ( . 129
33. 5 , 1 , 0 4 4 0 0
x y y y y y Koshi masalasining yecimini toping .
3 4 2 x e y . B) x e x y 2 ) 1 3 ( . C) x e x y 2 ) 1 7 ( . D) x x y 2 sin 4 2 cos . E) x e x x y 2 ) cos sin
3 ( . 34.
0 5 4
y y tenglamaning umumiy yechimini toping . A) x e C C y 2 2 1 . B) x e C x C y 2 2 1 ) ( . C) x e C x C y 2 2 1 ) ( . D) x e x C x C y ) 2 sin 2 cos ( 2 1 . E) x e x C x C y 2 2 1 ) cos sin ( . 35.
2 ) 0 ( , 4 ) 0 ( , 0 5 4 y y y y y Koshi masalasining yechimini toping .
2 3 . B) x e x y 2 ) 6 4 ( . C) x e x y 2 ) 4 10 ( . D) x e x x y ) 2 sin 3 2 cos 4 ( . E) x e x x y 2 ) cos 4 sin 10 ( .
36. 2 ) 0 ( , 4 ) 0 ( , 0 5 4 y y y y y Koshi masalasi yechimining x=π/2 nuqtadagi qiymati nimaga teng ?
e y 3 ) 2 / ( . B) e y ) 3 4 ( ) 2 / ( . C) e y 10 ) 2 / ( . D)
y 4 ) 2 / ( . E) e y ) 5 4 ( ) 2 / ( . II tartibli chiziqli o’zgarmas koeffitsientli bir jinslimas differensial tenglamalar 1. II tartibli chiziqli y′′+py′+qy=f(x) differensial tenglama qaysi shartda bir jinslimas deb ataladi ?
2. II tartibli chiziqli y′′+py′+qy=f(x) differensial tenglama qaysi holda birjinslimas bo‘lmaydi ?
3. II tartibli chiziqli y′′+py′+qy=(α 2 −1)f(x) differensial tenglama α parametrning qanday qiymatlarida birjinslimas bo‘ladi ? A) α >0 . B) α≠0 . C) α<0 . D) α≠±1 . E) α=±1 . 4. II tartibli chiziqli y′′+py′+qy=(α 2 −1)f(x) differensial tenglama α parametrning qanday qiymatlarida birjinslimas bo‘lmaydi ? A) α >0 . B) α≠0 . C) α<0 . D) α≠±1 . E) α=±1 . 130
5. Quyidagi II tartibli chiziqli tenglamalardan qaysi biri bir jinslimas bo’ladi? A) y′′+py′+qy=0 . B) y′′+py′+q=0 . C) y′′+py′=0 . D) y′′+qy=0 . E) keltirilgan barcha differensial tenglamalar bir jinslidir .
6. II tartibli bir jinslimas chiziqli y′′+py′+qy=f(x) differensial tenglamaning xususiy yechimi y*, unga mos keluvchi bit jinsli tenglamaning umumiy yechimi y 0
bo‘lsa, birjinslimas tenglamaninh umumiy yechimi y qanday ko‘rinishda bo‘ladi ? A) y= y*+ y 0 . B) y= y*/ y 0 . C) y= y*∙y 0 .
D) y=y 0 / y * . E) y= C 1
2
0 .
7. Agar II tartibli bir jinslimas chiziqli y′′+py′+qy=f(x) differensial tenglama mos keluvchi bir jinsli tenglamaning chiziqli erkli yechimlari y 1 va y 2 bo‘lsa, o‘zgarmaslarni variatsiyalash usulida bir jinlimas tenglamaning xususiy yechimi y* qanday ko‘rinishda izlanadi ? A) y*=C 1 (x) y 1 ∙ C 2 (x)
2 . B) y*=C 1 (x)
1 + C 2 (x)
2 . C) y*=C 1 (x)
1 / C 2 (x)
2 . D) y*=[C 1 (x)+C 2 (x)](
1 + y 2 ) . E) y*=[C 1 (x)–C 2 (x)]( y 1 – y 2 ) . 8. II tartibli bir jinslimas chiziqli y′′+py′+qy=f(x) differensial tenglamaning y* xususiy yechimini o’zgarmaslarni variatsiyalash usulida y*=C 1 (x)y 1 +C 2 (x)y 2
ko’rinishda izlanganda (bunda y 1 va y 2 tegishli bir jinsli tenglamaning chiziqli erkli yechimlari) noma’lum C 1 (x) va C 2 (x) funksiyalar qaysi sistemadan topiladi?
A)
0 ) ( ) ( ) ( ) ( ) ( 2 2 1 1 2 2 1 1
x C y x C x f y x C y x C . B) ) ( ) ( ) ( 0 ) ( ) ( 2 2 1 1 2 2 1 1 x f y x C y x C y x C y x C .
C) ) ( ) ( ) ( 0 ) ( ) ( 2 2 1 1 2 2 1 1
f y x C y x C y x C y x C .
D) 0 ) ( ) ( ) ( ) ( ) ( 2 2 1 1 2 2 1 1
x C y x C x f y x C y x C .
E) to’g’ri javob keltirilmagan.
9. O‘zgarmaslarni variatsiyalash usulida y′′–4y′+3y=xsin2x II tartibli chiziqli differensial tenglamaning xususiy yechimi y* qanday ko‘rinishda izlanadi ? A) y*=C 1 (x)e 2x +C 2 (x)e –2x . B) y*=C 1 (x)e x +C 2 (x)e –2x .
C) y*=C 1 (x)e x +C 2 (x)e 3x . D) y*=C 1 (x)sin2x+C 2 (x)cos2x . E) y*=C 1 (x)e x sin2x+C 2 (x)e 3x cos2x 10. Agar y′′+py′+qy=P n (x)e αx
(P n (x)–n-darajali ko‘phad) differensial tenglamada α soni λ 2 +pλ+q=0 xarakteristik tenglamaning ildizi bo‘lmasa va Q n (x) n-darajali ko‘phadni ifodalasa, unda differensial tenglamaning xususiy yechimi y* qanday ko‘rinishda izlanadi ? A)
) ( . B) x n e x xQ y ) ( . C) x n e x Q y ) ( . D) x n e x Q x y ) ( 2 . E) x n e x Q y ) ( 2 .
11. Agar y′′+py′+qy=P n (x)e αx
(P n (x)–n-darajali ko‘phad) differensial tenglamada α soni λ 2 +pλ+q=0 xarakteristik tenglamaning oddiy ildizlaridan biriga 131
teng bo‘lsa va Q n (x) n-darajali ko‘phadni ifodalasa, unda differensial tenglamaning xususiy yechimi y* qanday ko‘rinishda izlanadi ? A) x n e x Q y ) ( . B) x n e x xQ y ) ( . C) x n e x Q y ) ( . D) x n e x Q x y ) ( 2 . E) x n e x Q y ) ( 2 .
12. Agar y′′+py′+qy=P n (x)e αx
(P n (x)–n-darajali ko‘phad) differensial tenglamada α soni λ 2 +pλ+q=0 xarakteristik tenglamaning karrali ildizi bo‘lsa va Q n (x) biror n-darajali ko‘phadni ifodalasa, unda differensial tenglamaning xususiy yechimi y* qanday ko‘rinishda izlanadi ? A) x n e x Q y ) ( . B) x n e x xQ y ) ( . C) x n e x Q y ) ( . 0>0>0>0> Download 0.64 Mb. Do'stlaringiz bilan baham: |
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