Microsoft Word Birinchi tartibli chiziqli, Bernulli va Rikkati hamda to’la differensialli tenglamalar doc

dy = −y² + 2xy + (5 − x² ) dx

Rikkati tenglamasining umumiy yechimini toping.
4

1. 
   y = x + 2 ⁺ Cå₄x ₋₁
   

7

2. 
   y = x + 2 − Cå4x −3x
   

5

4. 
   y = x + 2 ⁺ _4÷ Cå −1
   

8

4. 
   y = x + 2 − Cå4x − 7x
   

III darajali testlar
7. Ushbu
x² −3y² 2y

dx + dy = 0

x4 x3
to’la differensialli tenglamaning umumiy yechimini toping.
1 y

1. 
   − ₃ = Ñ x x 1 y²
   
2. 
   − + = ^С x x3
   

4 y²

4. 
   ₂ ⁺ ₃ = Ñ x x
   

5 y²

4. 
   + ₃ = Ñ x x
   

8. y′ + ¹ y = x differensial tenglamaning umumiy yechimini toping.
x

1. 
   y=1₂+ x²  x 2 
   
2. 
   y=1_C− ^x2 _ x 2 
   

4. 
   y=1_C+ x²  x 2 
   
5. 
   y=−1_C+ x²  x 2 
   

40.6-ilova Mustaqil bajarish uchun topshiriqlar

1. 
   Quyidagi differensial tenglamalarning umumiy yechimlarini toping:
   

1) y′ − ytgx = ctgx; 2) y′+ ycos x = sin2x.

2. 
   (1− x²)y′ − xy = 2x differensial tenglamaning x = 2 bo’lganda y = 3 bo’ladigan xususiy yechimini toping.
   

3. 
   y′ + ^y = ^{x +}₅¹ tenglama uchun x =1 bo’lganda y = −1 boshlang’ich shart
   

3 3y
bajariladigan Koshi masalasini yeching.

4. 
   Ushbu to’la differensialli tenglamalarning umumiy yechimlarini toping:
   

1) 3( x²y − 4xy²)dx + (x³ − 4x²y +12y³)dy = 0 ; 2) 3x²å^y dx + (x å^{3 y} −1)dy = 0 .
5. Quyidagi differensial tenglamalar uchun integrallovchi ko’paytuvchilarni toping va tenglamalarning umumiy yechimlarini aniqlang:
1) (xcos y − ysin y)dx ⁺ (xsin y + ycos y)dy = 0 ; 2) 2xtgxdx + (x² − 2sin y)dy = 0.