1.2.6. Задание 6

n

F(x, y, y^/, y^//) = 0

Нач. усл.

n

F(x, y, y^/, y^//) = 0

Нач. усл.

1

y^/ = xy + x² + y²

y(0) = 1

13

y^/ = x² + 0,2y²

y(0) = 0,1

2

y^/ = e^3x +2xy²

y(0) = 1

14

y^/ = x² – xy + 2y

y(0) = 1

3

y^/ = x + e^y

y(0) = 0

15

y^/ = 2x + xy - y²

y(0) = 1

4

y^/ = x² + y²

y(0) = 0,2

16

y^/ = xy + x²

y(0) = 1

5

y^/ = x²- xy + y²

y(0) = 0,5

17

y^/ = -x³ - xy

y(0) = 3

6

y^/ =yCosx+2Cosy

y(0) = 0

18

y^/ = yCosx-Sin2x

y(0) = 3

7

y^/ = e^{Sin x} + x

y(0) = 0

19

y^/ = 4xy – 4x³

y(0)= -0,5

8

y(1) = 0

20

y^/= 0,2x – 0,1y²

y(0) = 1

9

y^/ =(1+x)y²e ^{- x}-xy

y(0) = 1

21

y^/= x²y² – y Cos x

y(0) = 1

10

y^/ = 4(x³+1) y² e^-x -4x³y

y(0) = 1

22

y^/= e ^{Sin x} + xy

y(0) = 0

11

y^/ = xy² - y

y(0) = 1

23

y^/= x² - xy

12

2(xy+y ^/)=(x-1)e^xy²

y(0) = 2

24

y^// + xy = 0

y(0) = 1

y^/(0) = 0

1

2

3

4

5

6

25

y^/ = 4y²e^4x (1- x³) - 4x³y

y(0)= -1

46

y^//= x²y + y

y(0) = 1

y^/(0) = 0

26

y^/= y + 2xy²

47

y^// = x + y²

y(0) = 0

y^/(0) = 1

27

y^/ = 2x³y³ – 2xy

48

y^// = x²y – y^/

y(0) = 1 y^/(0) = 0

28

4y^/=(x³+8)e^-2xy²-x²y

y(0) = 1

49

y^/ = e^y + xy

y(0) = 0

29

2y^/ = xy² –2y

y(0) = 2

50

y^/ = 2x - y

y(0) = 2

30

y^/ +xy =(x-1)e^xy²

y(0) = 1

51

y^/ = 2y² + ye^x

31

y^/ =xy² + y

y(0) = 1

52

y^/ = y² + x³

32

y^/ =xy + x² + y²

53

xy^// + y = 0

y(1) = 0

y^/(1) = 1

33

y^/ =xy + y²

54

y(1) = 1

y^/(1) = 0

34

y^/ = 2x – xy - 0,1y²

y(0) = 1

55

y^/ = arcsin y + x

35

y^/ = x + y + y²

56

y^/ = xy + Ln(x+y)

y(1) = 0

36

y^/=x² Sin x + y

y(0) = 1

57

y^/ = x + y ^{- 1}

y(0) = 1

37

y^/=x² + Sin x + y²

58

y^/ = 2x + Cos y

y(0) = 0

38

y^/=Cos y + 2x Cos x

y(0) = 0

59

y(0) = 1

39

y^/= y Sin x – 3Sin y

60

y^/+ y Cosx - 3e^xy² –Sinx = 0

y(0) = 1

40

y^/= e^2x - 2x²y

y(0) = 1

61

2y^/-(x+y)y-e^x=0

y(0) = 2

41

y^/= 2x² + ye^x

62

y^/-4y+2xy²-e^3x=0

y(0) = 2

42

y^/-4y+2xy²-e^3x=0

y(0) = 2

63

(1+x²) y^// + 5xy^/ + +3y = 0

y(0) = 0

y^/(0) = 1

43

y^// = y Cos y^/ + x

y(0) = 1

64

(1+x²)y^//+y=0

y(1) = 1

y^/(1) = 1

44

y^// = x² + y²

y(-1) = 2

65

(x² – x + 1)y^// + (4x-2)y^/ = -2

y(0) = 2

y^/(0) =1

45

y^// = ( y^/ )² + xy

y(0) = 4

y^/(0) = -2

66

(1 - x)y^// - y^/ + e^x (x+1) = 0

y(0) = 0

y^/(0) = 1

1

2

3

4

5

6

67

y(1) = 1

y^/(1) = 0

84

(1 - x²)y^// - 2xy^/ + +2y = 0

68

y^// = xyy^/

y(0) = 1

y^/(0) = 1

85

y^/// = y

y(0) = 1

y^/(0) = 0

y^//(0) = 0

69

y^/// = ye^x – x(y^/ )²

y(0) = 1

y^/(0) = 1

y^//(0) = 1

86

y^/// = xy^/ + y

y(1) = 1

y^/(1) = 0

y^//(1) =1

70

y^/// = y^//+(y^/ )²+y³+x

y(0) = 1

y^/(0) = 2

y^//(0)=05

87

y^///-x²y^//-xy^/-y=0

y(0) = 1

y^/(0) = 1

y^//(0) = 0

71

y^// = y

y(0) = 0

y^/(0) = 1

88

y^/ = arctg y + x

y(0) = 1

72

y^// + 2xy = 0

y(1) = 1

y^/(1) = 0

89

y^/ = e^{Cos x} + y

73

y^// - xy^/ - 2y = 0

y(1) = 0

y^/(1) = 1

90

y^/ = Siny + 2Cosx

y(0) = 0

74

y^// - x²y = 0

y(1) = 0

y^/(1) = 1

91

y^/=x+y+Ln(x+2y)

y(1) = 0

75

y^// + xy^/ + y = 0

y(0) = 1

y^/(0) = -1

92

y(0) = 1

76

(1-x²)y^//-4xy^/-2y=0

y(0) = 1

y^/(0) = 1

93

y^/ = x – arccosy

77

(1-x)y^//+xy^/-y=0

y(-1) = 0

y^/(-1) = 1

94

y^/ = e^y + Cosx

y(0) = 0

78

y^// + xy^/ = x

y(1) = 1

y^/(1) = 0

95

y^/+Ln(x+y)+x=0

y(0) = 1

79

y^/+(y+tgx)Cosx=0

y(0) = 1

96

xy^/ + x²y = Lnx

y(1) = 0

80

y^// + xy^/ + arctgx = y

y(0) = 1

y^/(0) = 1

97

y^// +x²y^/ - e^x = 0

y(0) = 1

y^/(0) = 0

81

e^xy^/ + yx² = e^x

y(0) = 1

98

(1 +x)y^/ + xe^y = 1

y(0) = 0

82

y^// + arctgx = y^/

y(0) = 0

y^/(0) = 1

99

y^/ = x²y + y³

y(1) = 1

83

xy^// + y^/ + y = e^x

y(1) = 0

y^/(1) = e

100

(1 - x)y^// + 4xy^/ + +y² = 0

y(0) = 1

y^/(0) = 2