Файл: В.М. Волков Математика. Программа, контрольные работы №7, 8 и методические указания для студентов-заочников инженерно-технических специальностей 2 курса.pdf

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≤ x ≤

π

a)∫∫xydxdy,D = y ≥ sin x,0

2

,y ≤ 3 .

144.

D

б)∫∫

R2 − x2 − y2

dxdy,D ={x2

+ y2 ≤ R2 ,y ≥ 0}.

a)∫∫D (2x + y)dxdy,D ={y ≥ x,1 ≤ x ≤ 3,y ≤ x + 5}.

145.

D

1 − x2 − y2 dxdy,D ={x2 + y2

≤1,x ≥ 0,y ≥ 0}.

б)∫∫

D

a)∫∫(x + y2 )dxdy,D ={y ≥ x3 ,y ≥ −x,y ≤1}.

146.

D

б)∫∫(x2 + y2 )4 dxdy,D ={x2

+ y2

≤1,y ≥ 0}.

D

a)∫∫xdxdy,D ={0 ≥ x ≤ 4,0 ≤ y ≤ 2x }.

147.

D

б)∫∫(x2 + y2 )5 dxdy,D ={x2

+ y2

≤1,y ≥ 0}.

D

y2

∫∫D

a)

x

dxdy,D ={y ≥ x,0

≤ x ≤ 5,y ≤ 3x}.

148.

∫∫

4 − x2 − y2 dxdy,D = {x2 + y2

≤ 4,y ≥ 0}.

б)

a)∫∫D (x + y)dxdy,D ={y ≤ ln x,x ≤ e,y ≥ 0}.

149.

D

б)∫∫

1

dxdy,D ={x2

+ y2

≤16,x ≥ 0,y ≥ 0}.

D

25 − x2 − y2

a)∫∫

≥

1

x

2

,y

≤

x

(x + 2y)dxdy,D = y

8

.

150.

D

б)∫∫(x2 + y2 )3 dxdy,D ={x2

+ y2

≤ 4,y ≥ 0}.

1.

y

− x = 0 .

16.

y2 + x2 y′ = xyy′.

y′ + x

2.

(x2 + y2 )dy = 2xydx .

17.

y′ −

1 − 2x

y = 1.

x2

61.

y′′ + 9y = cos3x, y(

0)= 2, y′(0)= 3.

62.

y′′ − 6y′ + 9y = 2e3x ,

y(0)= 1,

y′(0)= 0.

63.

y′′ − 2y′ + y = xex ,

y(0)= 5,

y′(0)= 3 .

38

64.

y′′ + y′ = x2 − 5,

y(0)= 0,

y′(0)= 2.

65.

y′′ + 4y′ + 29y = x2 − x,

y(0)= 5,

y′(0)= 0 .

66.

y′′ + 3y′ + 2y = 3e−x ,

y(0)= 1,

y′(0)= 4 .

67.

y′′ + 2y′ = x2 + 3x + 4,

y(0)= −1,

y′(0)= 4 .

68.

y′′ − y′ − 6y = −2e3x ,

y(0)= −3,

y′(0)= 1.

69.

y′′ + y′ − 2y = (x − 2)ex ,

y(0)= 3,

y′(0)= 0 .

70.

y′′ + y = 6cos2x − sin 2x,

y(π)= 1,

y′(π)= 1.

71.

y′′ − 4y′ + 13y = sin 3x,

y(0)

= 5

,

y′(0)

= 1 .

7

7

72.

2y′′ + 5y′ = 30x2 − 4,

y(0)= 4,

y′(0)=

5 .

73.

y′′ − y′ = e2x ,

y(0)= −3,

y′(0)= 1.

2

74.

y′′ + 2y′ + 5y = x2 − 3x,

y(0)= 4,

y′(0)= −2.

75.

y′′ − 3y′ = −3e3x ,

y(0)= −1,

y′(0)= 6.

76.

y′′ + 4y′ + 4y = 15e3x ,

y(0)= 1,

y′(0)= 3 .

77.

y′′ + y′ − 2y = 2ex ,

y(

0)= 4,

y′(0)= 1.

78.

y′′ − 5y′ + 6y = −3e−x ,

y(0)= 4,

y′(0)= 0 .

79.

4y′′ + 4y′ + y = x2 + x − 1,

y(0)= 5,

y′(

0)= 0,5 .

80.

y′′ + 2y′ + 2y = 2e2x ,

y(π)= −3,

y′(π)= 4 .

81.

y′′ − 2y′ − 3y = 8e3x ,

y(0)= 1,

y′(

0)= −2.

82.

y′′ − 4y = 4x2 + x − 8,

y(0)= 3,

y′(0)= 1.

83.

y′′ − y = 6ex ,

y(0)= 1,

y′(0)= −3 .

84.

y′′ + 5y′ + 6y = 10e2x ,

y(0)= 5,

y′(0)= −2.

85.

y′′ − 8y′ + 7y = 6xex ,

y(0)= 1,

y′(0)= 7.

86.

y′′ − 6y′ + 13y = x2 − x,

y(0)= −2,

y′(0)= 0 .

87.

y′′ − y = 8e3x ,

y(0)= 3,

y′(0)= −2.

88.

y′′ − 2y′ = 6x2 − 3,

y(

0)= 3,

y′(0)= −4 .

89.

y′′ + 4y = x2 − x + 1,

π

=

1,

y′(π)= 4 .

y

2