Комплексные переменные

Задача 14.Найти модуль и аргумент комплексного числа:

Задача 15. Вычислить

Задача 16. Найти все значения

Дифференциальные уравнения

17.1 xy^|+1 = e^y

17.2

17.3 (1+x²) y^||-2xy^| = 0

17.4 xy^|+1 = e^y

17.5

17.6

_17.7

17.8

_17.9.

_17.10

17.11 y^|-xy² = 2xy

17.12 xy^|+y = y², y(1)=0,5

_17.13

17.14 z^| = 10^x+z

_17.15

_17.16

17.17 2x²yy^|+y² = 2

17.18 y^| ctgx+y = 2, y(0)=-1

17.19 y^| sinx = y lny, y(/2)=1

17.20 x²y^| - cos2y = 1

2. 18.1

3. 18.2

4. 18.3

5. 18.4

6. 18.5

7. _18.6

8. 18.7

9. _18.8

13. 18.9 ydx – (x+y)dy = 0

14. 18.10(y²-3x²)dx – 2xydy = 0

15. 18.11 (x²+2xy-y²)dx+(y²+2xy-x²)dy = 0

16. _18.12

17. 18.13 (y²-2xy)dx+x²dy = 0

18. 18.14 y²+x²y^| = xyy^|

19. 18.15(x²+y²)y^| = 2xy

20. 18.16 xy^|-y=x

21. _18.17

22. _18.18

23. _18.19

24. _18.20

26. 19.1 (2x+1) y^| = 4x+2y

27. 19.2 x² dy = (2xy+x²-y)dx

28. 19.3 2x (x²+y) dx = dy

29. 19.4 xy^|+(x+1)y = 3x²e^-x

30. 19.5 (x+y²)dy = ydx

31. 19.6 (sin²y+x ctgy) y^| = 1

32. 19.7(2x+y) dy = ydx+4 lny dy

33. 19.8 xy dy = (y²+x) dx

34. 19.9 y^| x³ siny = xy^|-2y

35. 19.10 (xy+e^x) dx-x dy = 0

36. 19.11 y = x (y^|-x cosx)

37. 19.12 (xy^|-1) lnx = 2y

38. 19.13 2e^y-xy^| = 1

39. 19.14 xy²y^| = x²+y³

40. 19.15 xy^|-2x² = 4y

41. 19.16 2y^|-=

42. 19.17 (2x²y lny-x) y^| = y

43. 19.18 2xy^|-6y = -x²

19. y^|+y cosx = sinx cosx

44. 19.20(x+1)y^|=4x+2y

45. 20.1 2xy^| y^|| = y^|2-1

46. 20.2 y^|2+2yy^|| = 0

47. 20.3 yy^||+1=y^|2

48. 20.4 y^||| = 2(y^||-1) ctgx

49. 20.5 yy^|| = y^|2-y^|3

50. 20.6 2yy^|| = y²+y^|2

51. 20.7 y^||2+y^| = xy^||

52. 20.8 y^||+y^|2=2e^-y

53. 20.9 y^||2 = y^|2+1

54. 20.10 2y^| (y^||+2) = xy^||2

55. 20.11 y^|2 = (3y-2y^|) y^||

56. 20.12 y^|| (2y^|+x) = 1

57. 20.13 (1-x²) y^||+xy^| = 2

58. 20.14 yy^||-2yy^| lny = y^|2

59. 20.15 (y^|+2y) y^|| = y^|2

60. 20.16 xy^|| = y^|+x

61. 20.17 yy^||+y = y^|2

62. 20.18 2yy^|3+y^|| = 0

63. 20.19 y^|| (3y+4) – 3y^|2 = 0

64. 20.20 2xy^|y^|| = y^|2+1

67. 21.1 a) y^||+y^|-2y = 0

68. b) y^||+3y^|-4y = e^-4x+xe^-x

69. 21.2 a) y^||-2y = 0

70. b) y^||+2y^|-3y = x²e^x

71. 21.3 a) y^||-4y^|+5y = 0

72. b) y^||-4y^|+8y = e^2x+sin2x

73. 21.4 a) y^||+4y = 0

74. b) y^||-2y^|+y = 6xe^x

75. 21.5 a) 4y^||+4y^|+y = 0

76. b) y^||-y = 4shx

77. 21.6 a) y^|||-3y^||+3y^|-y = 0

78. b) y^||+4y^|+3y=chx

79. 21.7 a) y^|||-3y^|+2y = 0

80. b) y^||+2y^|+2y = xe^-x

81. 21.8 a) y^||+4y^|+3y = 0

82. b) y^||+y^| = 2cosx+e^x

83. 21.9 a) 2y^||-5y^|+2y = 0

84. b) y^||+y = 4sinx

85. 21.10 a) y^||+2y^|+10y = 0

86. b) y^||-3y^|+2y = x cosx

87. 21.11.a) y^||-2y^|+y = 0

88. b) y^||+y = 4xe^x

89. 21.12 a) y^|||-6y^||+9y^| = 0

90. b) y^||+y^|-2y = 3xe^x

91. 21.13 a) y^||+2y^|+y = 0

92. b) y^||-3y^|+9y = x cosx

93. 21.14 a) y^|||-y^||-y^|+y = 0

94. b) y^||-2y^|-3y = e^4x

95. 21.15 a) y^|||+8y^||+16y^| = 0

96. b) y^||-y = 2e^x-x²

97. 21.16 a) y^||+4y^|+3y = 0

98. b) y^||-3y^|+2y = sinx

99. 21.17 a) y^||+y^|-2y = 0

100. b) y^||-5y^| = 3x²+sin5x

101. 21.18 a) y^||-3y^|+2y = 0

102. b) y^||+y = x sinx

103. 21.19 a) y^||-5y^|+4y = 0

104. b) y^||-9y = e^3x cosx

105. 221.20a) y^||+2y^|-3y = 0

106. b) y^||+4y^|+4y = xe^2x