O'rta maxsus ta'lim

3х, у(1) = 1-

4 . 1 7 . У - - ^ = 1 + Х2, у { 1) = 3.

1 + х
у' + ~ ^ - у = 1, у ( \ ) = \.

4.19 , у + ^ = А ^ ( 1) = , .

X X
4.20. у ' + 2 ху - - 2 х 3, y ( l ) = е _ | .

4.21. / + - 7 ^ _ т - £ , >.(0 ) = —.

2 ( 1 - х 2 ) 2 ' ' з
4.22. у ' + ху = - х 3, у ( 0 ) = 3.

4.23. у — ( х + 1)2 , у ( 0 ) = 1.

4.24. У + 2 ху = x e ' x2 s in x , _у(0) = 1. 4.25. / - 2 > > / ( х + 1) = ( х + 1 ) \ у ( 0 ) = 1 /2 .

4.26. У - y c o s x = —s in 2 x , у ( 0 ) = 3. 4.27. У - 4 х _ у = - 4 х 3, у ( 0 ) = - 1 / 2 .
. У 1пх
4.28. y - L = -------- , у(1 ) = 1.
X X
4.29. У - З х 2у = х 2 (1 + х 3) / э , у ( 0 ) = 0.
4.30. y ~ j ' C o s x = s in 2 x , у ( 0 ) = —1.

4. 
   Koshi masalasining yechimini toping.
   

5.1. у 2dx + ( x + e 2^y ^dy = 0 , _y|^e = 2 . 5 . 2 . ( / е ' + 2 х ) у = * Я _0 = 1 .
5.3. / < / х + ( х у - l) rfv = 0, y\x^ = e .
5.4. 2 ( 4 / + 4 > > —х ) у = 1, 4 , о = 0 .
5.5. ( c o s 2 y c o s 2y - x ) y = sin> 'C O sy, y \ x=]/4 = я / 3 .
5.6. ( x c o s 2y - / ) / = .у c o s 2 у , у \ ^ = л / 4 .
5.7. ey2( d x - 2xydy) = ydy, > jr=0 = 0. 5.8. (10 4 / —x ) / = 4_y, y | ^ 8 = l .
5.9. dx + {xy —y 3}dy = 0, у |х^ . , = 0.
5.10. ( 3 y c o s 2 y - 2 y 2s \ n 2 y - 2 x ) y ' = у , y \xЧ6 = л / 4 .
5.11. S ( 4 y 3 + x y - y ) y ' = 1, Я =0 = 0 .
5.12. ( 2 ln у - In 2 y ) d y = y d x - x d y , = e 2 .
5.13.2(* + / ) У = ^, y\ I=. 2 = ~ l -
5.14. y 3( y - \) d x + Зху2 ( у - 1 )dy = ( y + 2 )dy, y\x=yi = 2.
5.15. 2 y 2d x + ( x + ^ ly}dy = 0 , = 1.

5.16. {xy + y[y} dy + y 2dx = 0, ^ L _ 1/2= 4 -

5.17. s m ly d x = {s\n22 y - 2 s m 2y + 2 x ) dy, у\х^ г = n j4 .
5.18. { y 2 + 2 y - x ) y ' = 1, у\х Л = 0 .
5.19. 2 y j y d x - [ 6 x y ] y + l^ d y = Q, y\x_ 4 = \-

20. 
    c?x = ( s i n y + 3 c o s j + 3x)c?y, у \х=к.ц = n /2 .
    
21. 
    2 ( c o s 2 у ■cos2_y - x ) У = s i n 2 y, y \x^jn = 5 x /4 .
    
22. 
    chydx = ( l + xsh x^d y , y\x=i= \n 2 .
    

5.23. ( l Ъуъ —j r ) y = 4 y, >'|I=5 = 1 -
5.24. y 2 ( y 2 + 4 )dx + 2x y ( y 2 + 4 )dy = 2dy, у\х_ф = 2. 5.25. ( x + \n 2 y - \ n y ) y ' = y / 2 , y\x=2= \-
5.26. (2 xy + 4 y ) d y + 2y 2dx = 0, y\x ]/2 = 1.
5.27. ydx + ( 2 x - 2 s in 2 > - y s i n 2 y} dy = 0 , у\х^ г = я / 4 .
5.28. 2 (у* - у + xy) dy = dx, y\^_ 2 = 0 .
5.29. ( l y + x t g y - y 2tg y ) d y = dx, у\г^ = я .
5.30. 4 y 2dx + (e;l(ly)+ x} dy = 0, y\x=c = 1 / 2 .

4. 
   Koshi masalasining yechimini toping.
   

6Л. y ' + xy = ( \ + x ) e x y 2, j ( 0 ) = l .
6.2. xy' + у = 2 y 2 In x , _y(l) = 1/ 2 .

6.3. 2 ( xy' + y ) = xy 2, у ( l ) = 2 .

6.4. y ' + 4 x 3y = 4 ( x 3 + l ) e ”4jr y 2, y ( 0 ) = 1.
6.5. xy' —у = —у 2 ( ln x + 2 ) ln x , y ( l ) = l . 6.6. 2 ( j / + л у ) = ( l + x ) e x y 2, y ( 0 ) = 2 . 6.7. 3 ( x y '+ y ) = y 2 inx, y ( l ) = 3 .
6.8. 2 y' + у co s x = у 1c o s x ( l + s i n x ) , y ( 0 ) = 1 . 6.9. у + 4 x 3y = 4 y 2e4x( l - x 3) , y ( 0 ) = - l .
6.10. 3у + 2 xy = 2xy~2 e~2x , y ( 0 ) = - 1.
6. 11. 2 xy - Ъ у = - ( 5 x 2 + з)>>3, >’( l ) = l/> /2 .
6. 12. 3 xy'+ 5 y = ( 4 x - 5 ) y 4, _y(l) = l.
6.13. 2 y ' + 3 y c o s x = e 2* ( 2 + 3 c o s x ) j '~ 1, _y(0) = l. 6.14. 3 ( x y '+ y ) = xy 2, y ( l ) = 3.
6.15. y ' —y = 2 xy 2, y ( 0 ) = l / 2 .
6.16. 2 x y '- 3 y = - ( 2 0 x 2 + 12 )y 3, y ( 1) = l / 2 V 2 .
6.17. y ' + 2 xy = 2 x 3y 3, у ( 0 ) = л/2.
6.18. xy’ + у = y 2\nx, y ( l ) = l.
6.19. 2 y ' + 3 y c o s x = (8 + l 2 c o s x ) e 2jry “1, y ( 0 ) = 2.
6.20. 4 / + x 3y = ( x 3 + 8 ) e 2x y 2, y ( 0 ) = l .
6.21. %xy - \ 2 y = - ( S x 2 + 3 ) y 3, _y(l) = -s/2 .
6.22. 2 ( y ' + y ) = xy 2, y ( 0 ) = 2 .
6.23. + = ( x - l ) e J' y 2, y ( 0 ) = l.
6.24. 2 / + 3 y c o s x = - e 2jr( 2 + 3 c o s x ) y v ( 0 ) = 1. 6.25. y ' - y = xy 2, > ( 0 ) = 1.
6.26. 2 ( x y '+ y ) = y 2lnx, y ( l ) = 2 .
6.27. y ' + у = xy 2, у ( 0 ) = 1.
6.28. y ' + 2 y c \ h x = y 2chx, y ( l ) = l / s h l . 6.29. 2 ( y ' + xy) = ( x - \ ) e * y 2, y ( 0 ) = 2. 6.30. y ' —y tg x = - ( 2 / 3 ) y 4s in x , 7 ( 0 ) = I .

4. 
   Differensial tenglamaning umumiy integralini toping.
   

7.1. 3 x 2 ey dx + ( x 3ey- t y d y = 0 .

7.2.
^/ 2x

3 x 2 + —cos
, 2 x 2 x
a x ----- - c o s — dy = 0 .

V У У ^{У У}
7.3. (3 x 2 + 4 y 2}dx + (&xy + ey } dy = 0.

7.4. ^ 2 x - 1 - jci!x - ^ 2 y - —ja fy = 0.

7.5. ( y 2 + ysec2 x} dx + ( 2 xy + tgx) = 0.

2
7.6. (3x 2y + 2y + 3)dtc + (x 3 + 2x + 3y2)c/y = 0.

1 1

7. 
   г H h ■
   

dx + ^{У x}


dy = 0 .

4 7 7 7 x y ) { 4 7 7 7 x у

7. 
   [ s in 2 x - 2 c o s ( x + y ) \ d x - 2 c o s ( x + y ) d y = 0. 7.9. ( x y 2 + x j y 2}dx + ( x 2y - x 2/ y 3) dy = 0.
   

7.10. d x - ^ - d y = 0 . x

7.11. - ^ - c o s —d x~ \ —c o s — + 2 y x x ( x X
dy = 0.

7.12.

• 
  J S + y
  

*+ y
лс+ c/y = 0 .

V*'+/J

7.13.
1 + J» '. Л + ., - ^
xy
dy = 0.

7.14.
dx x + y 2