8.2.3. Варианты заданий

№

Задача Коши

1

y'+xy = 0,5(x -1)e x y 2 ,

y(0) = 2;

a = 0, b = 2.

2

y'-ytgx = -2 / 3y4 sin x ,

y(0) =1;

a = 0, b =1,2.

3

y'+y 2 = x,

y(0) =1;

a = 0 ,

b = 2 .

4

xy'+y = y3e-x , y(1) = 1;

a = 1,

b = 2.

5

y'+xy = 0,5(x + 1)e x y 2 ,

y(0) = 1;

a = 0;

b = 2.

6

xy'-y = -y2 (2ln x + ln2 x),

y(1) = 2;

a = 1,

b = 2.

7

y'+4x3 y = 4 y2e4 x (1 - x3 ) ,

y(1) = 1;

a = 1,

b = 2,8.

8

2 y'+3 y cos x = e2 x (2 + 3 cos x) / y ,

y(1) = 2 ;

a = 1,

b = 1,6 .

9

y'+2xy = 2x3 y3 ,

y(0) =1;

a = 0, b =1.

10

xy'+ y = y 2 ln x ,

y(1) = 0,5;

a =1,

b = 5.

11

2 y'+3y cos x = (8 +12cos x)e2 x / y,

y(0) = 2; a = 0, b = 2.

12

4 y'+x3 y = (x3 + 8)e-2x y 2 ,

y(0) = 0,5; a = 0, b = 2,4.

13

8xy'=12 y = -(5x2 + 3) y3 ,

y(1) =1;

a =1, b = 3.

14

y'+ y = 0,5xy2 , y(0) = 2;

a = 0, b = 2.

15

y'+xy = (x -1)e x y2 ,

y(0) =1;

a = 0, b = 2.

16

3y'-3y cos x = -e-2 x (2 + 3 cos x) / y,

y(0) = 1,1;

a = 0 , b = 0,8.

17

y'- y = xy 2 ,

y(0) = 0,5;

a = 0,

b = 0,8.

18

xy'+ y = y 2 ln x ,

y(1) =1;

a =1,

b = 2,6.

19

y'+ y = xy 2 ,

y(0) =1;

a = 0,

b = 2.

20

xy'+ y = xy2 ,

y(1) =1;

a =1, b = 2.

21

2 y'+3y cos x = e2 x (2 + 3cos x) / y ,

y(0) =1;

a = 0, b =1,6.

22

3( xy'+ y) = xy 2 ,

y(1) =1;

a =1,

b = 5.

23

y'-y = 2xy 2 , y(-1) = 0,2;

a = -1, b = 0,6.

24

2xy'-3y = -(20x2 +12) y3 ,

y(1) = 0,25;

a =1, b = 5.

25

2 y'+3y cos x = (8 +12 cos x)e 2 x

/ y,

y(0) = 3;

a = 0 ,

b = 3.

26

y'+xy = (1 + x)e x y -2,

y(0) =1,

a = 0,

b = 1,6 .

27

xy'+ y = 2 y 2 ln x ,

y(1) = 0,5 ;

a =1,

b = 5

28

2xy'+2 y = xy 2 ,

y(1) = 2 ;

a =1,

b =1,8.

29

y'+4x 3 y = 4(x3 + 1)e -4 x y 2 ,

y(0) = 0,5 ;

a = 0 ,

b = 1.

30

xy'-y = -y 2 (2ln x + ln 2 x),

y(1) =1;

a =1,

b = 3.