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
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DIFFERENSIAL TENGLAMALAR 1.Differensial tenglamalar va ular bilan bog’liq tushunchalar
1. Differensial tenglama ta’rifini ko‘rsating . A) noma’lum funksiya qatnashgan tenglama . B) noma’lum funksiyaning turli qiymatlari qatnashgan tenglama . C) noma’lum funksiyaning hosilalari qatnashgan tenglama .
0 nuqtadagi qiymatlari qatnashgan tenglama . E) noma’lum funksiya va uning integrallari qatnashgan tenglama .
2. Quyidagilardan qaysi biri differensial tenglama bo‘ladi ? A) y 2 +5y–3cosx=0 . B) 3x 2 +4xy–1=0 . C) y(x)+2 y′(x 0 )–x=0 . D) y–2xy′+5=0 . E) 0 ) sin(
x ydx .
3. (α
2 −1)y′+αy+5x+9=0 tenglama α parametrning qanday qiymatlarida differensial tenglama bo’ladi? A) α≠0 . B) α≠1 . C) α≠−1 . D) α≠±1 . E) α (−∞, ∞) . 4. (α
2 −1)y′′+αy′+5xy+7=0 tenglama α parametrning qanday qiymatlarida differensial tenglama bo’ladi? A) α≠0 . B) α≠1 . C) α≠−1 . D) α≠±1 . E) α (−∞, ∞) . 5. Ta’rifni to‘ldiring: Differensial tenglamaning tartibi deb unda qatnshuvchi noma’lum funksiya hosilalarning ……… aytiladi . A) eng katta darajasiga . B) eng katta tartibiga . C) soniga . D) eng katta qiymatiga . E) to‘g‘ri javob keltirilmagan .
6. (y′) 3 –(y′) 2 + y′′–y+5y 4 +x 5 =0 differensial tenglama nechanchi tartibli ? A) I . B) II . C) III . D) IV . E) V .
7. (α 2 −1)y′′+αy′+5xy+7=0 differensial tenglama I tartibli bo’ladigan α parametrning barcha qiymatlarini ko’rsating. A) α=0 . B) α=1 . C) α=−1 . D) α=±1 . E) α (−∞, ∞) . 8. (α
2 −1)y′′+αy′+5xy+7=0 differensial tenglama II tartibli bo’ladigan α parametrning barcha qiymatlarini ko’rsating. A) α≠0 . B) α≠1 . C) α≠−1 . D) α≠±1 . E) α (−∞, ∞) . 9. n tartibli differensial tenglama eng umumiy holda qanday ko‘rinishda bo‘ladi ? A) F(y,y′, ..., y (n) )=0 . B) F(x, y,y′, ..., y (
)= y (n) . C) F(x, y,y′, ..., y (
, y (n) )=0 .
D) F(y,y′, ..., y (n) )= x . E) F(x, y,y′, ..., y (
)=0 .
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10. Biror y=φ(x) funksiya F(x, y,y′, ..., y (
, y (n) )=0 differensial tenglamaning yechimi bo’lishi uchun qaysi shart talab etilmaydi? A) y=φ(x) funksiya biror chekli yoki cheksiz D oraliqda aniqlangan . B) y=φ(x) funksiya D oraliqda n marta differensiallanuvchi . C) y=φ(x) funksiya D oraliqda monoton . D) y=φ(x) funksiya va uning y (k) (x)=φ (k) (x) (k=1,2, ... , n) hosilalari differensial tenglamani ayniyatga aylantiradi; E) keltirilgan barcha shartlar talab etiladi . 11. Differensial tenglamaning yechimi yana nima deb ataladi ? A) ildiz . B) differensial .
C) boshlang’ich funksiya . D) integral . E) tenglashtiruvchi funksiya .
12. Qyuidagi funksiyalardan qaysi biri y′−2y=0 differensial tenglamaning yechimi bo’ladi? A) y=x 2 .
B) y=sin2x . C) y=cos2x . D) y=e 2x . E) y=ln2x . 13. Qyuidagi funksiyalardan qaysi biri y′′+4y=0 differensial tenglamaning yechimi bo’ladi? A) y=x 4 .
B) y=2x 2 . C) y=cos2x . D) y=e 2x .
E) y=ln2x .
14. Qyuidagi funksiyalardan qaysi biri y′′+4y=0 differensial tenglamaning yechimi bo’lmaydi? A) y=sin2x . B) y=cos2x .
C) y=cos2x+sin2x . D) y=cos2x−sin2x .
E) y=cos2x∙sin2x . 15. Qyuidagi funksiyalardan qaysi biri y′′−4y=0 differensial tenglamaning yechimi bo’ladi? A) y=x 2 .
B) y=sin2x . C) y=cos2x . D) y=e 2x . E) y=ln2x . 16. λ parametrning qanday qiymatida y=e λx funksiya y′−4y=0 differensial tenglamaning yechimi bo’ladi? A) λ=2 . B) λ=−2 . C) λ=4 .
D) λ=−4 . E) λ=±1 .
17. λ parametrning qanday qiymatida y=e λx funksiya y′′−4y=0 differensial tenglamaning yechimi bo’ladi? A) λ=1 . B) λ=−1 . C) λ=4 .
D) λ=−4 . E) λ=±2 .
18. Qyuidagi funksiyalardan qaysi biri y′′′−6=0 differensial tenglamaning yechimi bo’ladi? A) y=x 4 .
B) y=x 3 . C) y= x 2 .
D) y=x . E) y=1/x .
19. n-tartibli F(x, y, y′, ..., y ( n−1) , y (n) )=0 differensial tenglama uchun boshlang‘ich shartlar qanday ko‘rinishda bo‘ladi ? A)
1 1 2 2 1 1 0 0 ) ( , , ) ( , ) ( , ) (
n y x y y x y y x y y x y . 117
B) ) 1 ( 1 1 ) 1 ( 2 2 1 1 0 0 ) ( , , ) ( , ) ( , ) ( n n n n y x y y x y y x y y x y . C) ) 1 ( 0 0 ) 1 ( 0 0 0 0 0 0 ) ( , , ) ( , ) ( , ) ( n n y x y y x y y x y y x y . D) 1 0 1 2 0 2 1 0 1 0 0 0 ) ( , , ) ( , ) ( , ) ( n n y x y y x y y x y y x y . E) 1 1 1 2 2 2 1 1 1 0 0 0 ) ( , , ) ( , ) ( , ) (
n n y x y y x y y x y y x y . 20. Differensial tenglamalar nazariyasidagi mavjudlik va yagonalik teoremasi qaysi matematik nomi bilan yuritiladi ? A) Lagranj . B) Laplas . C) Koshi . D) Bernulli . E) Rikkati . 21. y (n) =f(x, y, y′, ..., y (
) differensial tenglama uchun Koshi teoremasida tenglamaning o’ng tomonidagi funksiyadan qaysi shart talab etilmaydi ? A) bu funksiya biror ) ,
, , ( ) 1 ( 0 0 0 0 0 n y y y x M nuqta atrofida aniqlangan . B) bu funksiya ) , , , , ( ) 1 ( 0 0 0 0 0
y y y x M nuqta atrofida uzluksiz . C) M 0 nuqta atrofida x f xususiy hosila mavjud va u uzluksiz . D) M 0 nuqta atrofida uzluksiz ) 1 ( , , ,
y f y f y f xususiy hosilalar mavjud . E) Keltirilgan barcha shartlar talab etiladi .
22. n-tartibli differensial tenglama uchun Koshi masalasi Koshi teoremasi shartlarida nechta yechimga ega ? A) bitta . B) kamida bitta . C) n ta . D) kamida n ta . E) cheksiz ko’p .
23. Qyuidagi funksiyalardan qaysi biri y′−2y=0, y(0)=1 Koshi masalasining yechimi bo’ladi? A) y=1+x 2 .
B) y=1+sin2x .
C) y=cos2x . D) y=e 2x . E) y=lg(10+x) . 24. y=y(x, C 1 , C 2 , ..., C n ) funksiyalar sinfi n-tartibli differensial tenglamaning umumiy yechimi bo’lishi uchun quyidagi shartlardan qaysi biri talab etilmaydi ? A) bu funksiyalar n marta differensiallanuvchi . B) bu funksiyalar C 1 , C 2 , ..., C n o’zgarmaslarning ixtiyoriy qiymatlarida chegaralangan . C) bu funksiyalar C 1 , C 2 , ..., C n o’zgarmaslarning ixtiyoriy qiymatlarida berilgan differensial tenglamaning yechimi bo’ladi . A) bu funksiyalar C 1 , C 2 , ..., C n o’zgarmaslarning ma’lum bir qiymatlarida ixtiyoriy boshlang’ich shartlani qanoatlantiradi . B) keltirilgan barcha shartlar talab etiladi .
25. n-tartibli differensial tenglama uchun qanday yechim tushunchasi aniqlanmagan ? A) umumiy yechim . B) xususiy yechim . C) umumiy integral .
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D) maxsus yechim . E) normal yechim .
26. n-tartibli differensial tenglama umumiy integrali qanday ko’rinishda bo’ladi? A) Ф((x, C 1 , C 2 , ..., C n )−y=0 . B) Ф((x, C 1 , C 2 , ..., C n )+y=0 . C) Ф((x, y)=0 . D) Ф((x, y, C 1 , C 2 , ..., C n )=0 . E) Ф((y, C 1 , C 2 , ..., C n )±x=0 .
27. n-tartibli differensial tenglamaning umumiy y=y(x, C 1 , C 2 , ..., C n ) yechimlaridan qaysi holda maxsus yechim kelib chiqadi ? A) C 1 = C 2 = ...=C n . B) C 1 = C 2 = ...=C n =0 . C) 0 2
2 2 1 n C C C . D) C 1 = C 2 = ...=C n =1 . E) to’g’ri javob keltirilmagan . 2. I tartibli differensial tenglamalar
1. I tartibli differensial tenglama eng umumiy holda qanday ko‘rinishda bo‘ladi ? A) F(x,y,y′)=0 . B) F(x,y)= y′ . C) F(x, y′)= y . D) F(y,y′)= x . E) F(x,y,y′, y′′)=0 .
2. I tartibli differensial tenglama uchun boshlang‘ich shart qanday ko‘inishda bo‘ladi ? A) y(x 0 )= y 0 . B) y′(x 0 )= y 0 . C) 0 )
lim 0
x y x x . D) 0 0
( max
0 y x y x x . E) 0 0
( min
0 y x y x x .
3. I tartibli differensial tenglama uchun Koshi masalasini ko‘rsating . A) y′=f(x,y) , y′(x 0 )= y 0 . B) y′=f(x,y) , y(x 0 )= y 0 . C) y′=f(x 0 ,y) . D) y′=f(x,y 0 ) . E) y′=f(x 0 ,y 0 ) . 4. I tartibli tenglama uchun Koshi masalasi Koshi teoremasi shartlarida nechta yechimga ega ? A) kamida bitta . B) ko‘pi bilan bitta . C) faqat bitta . D) cheksiz ko‘p . E) yechimga ega emas .
5. I tartibli eng sodda differensial tenglama qanday ko‘rinishda bo‘ladi ? A) y′=f(x,y) . B) y′=f(y) . C) y′=f(x) . D) y′=f(y′) . E) y′=0 .
6.
I tartibli eng sodda y′=xe x differensial tenglamani integrallang . A) y=xe
D) y=(x–2)e x +C . E) y=(x+2)e x +C .
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7. I tartibli eng sodda y′=xe x differensial tenglama umumiy yechimining x=1 nuqtadagi qiymati y(1) uchun qaysi javob to’g’ri ? A) y(1)=0 . B) y(1)>0 . C) y(1)<0 . D) y(1)≠0 . E) y(1)=C , C –ixtiyoriy chekli son .
8. y′=xe x , y(0)=2 Koshi masalasini yechimini toping . A) y=xe
D) y=(x–2)e x +4 . E) y=(x+2)e x .
9.
I tartibli o‘zgaruvchilari ajralgan differensial tenglamani ko‘rsating . A) y′=f(xy) . B) y′=f(x/y) . C) y′+P(x)y=Q(x) . D) M(x)dx+N(y)dy=0 . E) M 1 (x) N 1 (y)dx+ M 2 (x)N 2 (y)dy=0 . 10. O‘zgaruvchilari ajralgan 0
y dy x dx differensial tenglamaning umumiy integralini toping. A) C y x 2 2
C y x . C) C y x 2 2
D)
2 2 4 . E) C x y y x .
11. I tartibli o‘zgaruvchilari ajraladigan differensial tenglamani ko‘rsating . A) y′=f(xy) . B) y′=f(x/y) . C) y′+P(x)y=Q(x) . D) M(x)dx+N(y)dy=0 . E) M 1 (x) N 1 (y)dx+ M 2 (x)N 2 (y)dy=0 . 0> Download 0.64 Mb. Do'stlaringiz bilan baham: |
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