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Froggy Jumps
Froggy Jumps

Differensial tenglamalar

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Differensial tenglamalar

Froggy Jumps

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About this activity

Bir jinslimas ikkinchi tartibli chiziqli tenglamalar.

Created by

Sevinch Rustamova
Sevinch Rustamova
Uzbekistan

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Differensial tenglamalar
 

Froggy Jumps

Differensial tenglamalarOnline version

Bir jinslimas ikkinchi tartibli chiziqli tenglamalar.

by Sevinch Rustamova
1

Ikkinchi tartibli bir jinsli chiziqli differensial tenglamaning umumiy ko‘rinishi qaysi?

2

y'' + py' + qy = 0 tenglamaning xarakteristik tenglamasi qanday yoziladi?

3

Agar xarakteristik tenglamaning diskriminanti D > 0 bo‘lsa, umumiy yechim qaysi ko‘rinishda bo‘ladi?

4

y'' - 5y' + 6y = 0 tenglamasining xarakteristik ildizlarini toping.

5

Agar xarakteristik tenglama ildizlari k₁= k₂=k (karrali ildiz) bo‘lsa, umumiy yechim qanday bo‘ladi?

6

y'' + 4y = 0 tenglamasining umumiy yechimini ko‘rsating.

7

Xarakteristik tenglamaning ildizlari k₁,₂= α±iβ(kompleks) bo‘lsa, yechim qanday ko‘rinishda bo‘ladi?

8

y'' - 4y' + 4y = 0 tenglamasining xarakteristik ildizi nimaga teng?

9

y₁(x) va y₂(x) funksiyalar chiziqli erkli bo‘lishi uchun ularning Vronskiy determinanti qanday bo‘lishi kerak?

10

y'' + 9y = 0 tenglamasining xarakteristik ildizlari qanday?

11

y'' - y = 0 tenglamasining umumiy yechimi qaysi?

12

Agar xarakteristik tenglama k² - 2k + 5 = 0 bo‘lsa, α va βnechaga teng?

13

y'' - 3y' = 0 tenglamasining xarakteristik ildizlari qanday?

14

Ikkinchi tartibli chiziqli bir jinsli differensial tenglamada y₁ va y₂ yechim bo‘lsa, y = C₁y₁ + C₂y₂ham yechim bo‘ladimi?

15

y'' + 2y' + 2y = 0 tenglamasining umumiy yechimini ko‘rsating.

 
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