Birinchi tartibli chiziqli differensial tenglamalar

1. Quyidagi differensial tenglamalarning umumiy yechimlarini toping:
1) ( ) 1 22 =+′+ xyyxa ; 2) ( ) xyyx =+′+12 .
2. 1+=+′ xyyx differensial tenglamaning 2=x da 3=y bo’ladigan boshlang’ich shartlarni qanoatlantiruvchi xususiy yechimini toping. 3. 2 3 x y x y y =+′ differensial tenglamaning 1−=x bo’lganda 1=y bo’ladigan xususiy yechimini toping.
4. Ushbu( ) ( ) 023232 2222 =+++ dyyyxdxxxy to’la differensialli tenglamaning umumiy yechimini toping.
5. ( ) 01 2 =−+ dyxydxy differensial tenglama uchun integrallovchi ko’paytuvchini toping va tenglamaning umumiy yechimini aniqlang.
4-varaqa
1. Quyidagi differensial tenglamalarning umumiy yechimlarini toping:
1) ctgxytgxy =−′ ; 2) .2sincos xxyy =+′ 2. 5=−′ yyx differensial tenglamaning 2=x da 3=y bo’ladigan boshlang’ich shartlarni qanoatlantiruvchi xususiy yechimini toping.
3. 1) 2 2 x y x y y =+′ differensial tenglamaning 3=x bo’lganda 4=y bo’ladigan xususiy yechimini toping.
4. Ushbu( ) ( ) 03223 2 =−++ dyxdxyx to’la differensialli tenglamaning umumiy yechimini toping.
5. ( ) 0cossin =++ dyxdxåx y differensial tenglama uchun integrallovchi ko’paytuvchini toping va tenglamaning umumiy yechimini aniqlang.


Adabiyotlar
1. Salahiddinov M. S. Nasriddinov G.N. Oddiy differinsial tenglamalar, Toshkent, ,,O‘zbekiston’’, 1994 y
2. Qori – Niyoziy T.N. Tanlangan asarlar, 4-tom, Differinsial tenglamalar, Fan, Toshkent, 1968 y

3. 
   Pontryachin L.S.Obknovenne differinsial uravneniya, M.1969 y
   
4. 
   Stepanov V. V Kurs differinsial uravneniy, Giz.fiz.mat. literature, 1958
   
5. 
   Yerugen N.P.i.dr. Kurs obknobennx differinsialnx uravneniy, Kiev, 1974 y
   
6. 
   Trikomi F. Differinsialne uravneniya, Izd. I.L. M.1962 y
   
7. 
   Samoylenko A. M. i.dr Differinsialne uravneniya; premir i zadachi, M 1989 y
   
8. 
   Guter R.S. Yanpoliskiy A.R.Differinsial tenglamalar, T 1973 y
   
9. 
   Petroviskiy I.G. Lektsin po teorin obkvonnex differinsialnx uravneniy M.Nauka 1964 y
   
10. 
    Xartman F.Obknovenne differinsialne uravneniya, izd. ,,Mir”, M 1970 y
    
11. 
    Koddinchton E.A.Lebisson G. Teoriya obknovenne differinsialnx uravneniy, M. IL. 1958 y
    
12. 
    Elischolis L.E. Differinsialnx uravneniya I variatsionnoe ischesliniya, Nauka, Moskva, 1965 y
    
13. 
    R.S.Gaute, A.R. Yanpoliskiy ,,Differinsial tenglamalar “ T 1978 y
    
14. 
    Fediryuk M.V. Obknovenne differinsialne uravneniya, M.1980 y
    

Xulosa
Birinchi tartibli differensial tenglamalarning muhim sinflaridan biri Bernulli differensial tenglamasi va uni yechishda muhim rol o‘ynaydigan birinchi tartibli chiziqli differensial tenglamani yechishni turli usullarini o‘rganish muhim ahamiyatga egadir.
Bernulli differensial tenglamasini yechimini mavjudligi va yagonaligi haqidagi teoremaning isboti keltiriladi, shuningdek bu tenglamaning maxsus yechimi masalasi ham o‘rganiladi.
Bernulli differensial tenglamasiga keltirib yechiladigan tenglamalarning sinflari (Darbu, Yakobi va Rikkate differensial tenglamalari) o‘rganiladi va bu hollarga doir aniq misollarni yechish ko‘rsatiladi.

3