Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 25 стр.

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27. ∆u(x, y) = 2,
u(0, y) = y + y
2
, u
x
(a, y) = 1,
u
y
(x, 0) = 0, u
y
(x, b) = 2b.
28. ∆u(x, y) = 4,
u
x
(0, y) = 2y, u(a, y) = 2a
2
,
u
y
(x, 0) = 2x
2
, u
y
(x, b) = 1 + 2x
2
.
29. ∆u(x, y) = 2 + 6y,
u
x
(0, y) = 0, u
x
(a, y) = 1,
u(x, 0) = 3x, u
y
(x, b) = 2b + 3b
2
.
30. ∆u(x, y) = 2 + 12x
2
,
u
x
(0, y) = 0, u
x
(a, y) = 2a + 4a
3
,
u
y
(x, 0) = 2x, u(x, b) = 1 + x
2
+ x
4
.
31. ∆u(x, y) = 2,
u
x
(0, y) = 0, u(a, y) = y + a
2
,
u
y
(x, 0) = 1, u(x, b) = x
2
+ b.
32. ∆u(x, y) = 4 + 6y,
u
x
(0, y) = 2, u(a, y) = 2y
2
+ y
3
+ a,
u
y
(x, 0) = 0, u(x, b) = x + 2b
2
+ b
3
.
33. ∆u(x, y) = 2,
u(0, y) = 1 + 2y + y
2
, u
x
(a, y) = 0,
u(x, 0) = 1, u
y
(x, b) = 1 + 2b.
34. ∆u(x, y) = 4 + 6x,
u(0, y) = 2, u
x
(a, y) = 2 + 4a + 3a
2
,
u(x, 0) = 2 + x + 2x
2
+ x
3
, u
y
(x, b) = 0.
35. ∆u(x, y) = 2,
u
x
(0, y) = 1, u(a, y) = 1 + y + a
2
,
u(x, 0) = 1 + x
2
, u
y
(x, b) = 0.
36. ∆u(x, y) = 2 + 6y,
u
x
(0, y) = 2y, u(a, y) = 3 + y
2
+ y
3
,
u(x, 0) = 3, u
y
(x, b) = 1 + 2b + 3b
2
.
37. ∆u(x, y) = 2 + 12x
2
,
u(0, y) = 1, u
x
(a, y) = 3y + 2a + 4a
3
,
u
y
(x, 0) = 2, u(x, b) = 1 + x
2
+ x
4
.
38. ∆u(x, y) = 2,
u(0, y) = 1, u
x
(a, y) = 1 + 2a,
u
y
(x, 0) = 0, u(x, b) = 1 + 3x + x
2
.
25
27. ∆u(x, y) = 2,
    u(0, y) = y + y 2 , ux (a, y) = 1,
    uy (x, 0) = 0, uy (x, b) = 2b.

28. ∆u(x, y) = 4,
    ux (0, y) = 2y, u(a, y) = 2a2 ,
    uy (x, 0) = 2x2 , uy (x, b) = 1 + 2x2 .

29. ∆u(x, y) = 2 + 6y,
    ux (0, y) = 0, ux (a, y) = 1,
    u(x, 0) = 3x, uy (x, b) = 2b + 3b2 .

30. ∆u(x, y) = 2 + 12x2 ,
    ux (0, y) = 0, ux (a, y) = 2a + 4a3 ,
    uy (x, 0) = 2x, u(x, b) = 1 + x2 + x4 .

31. ∆u(x, y) = 2,
    ux (0, y) = 0, u(a, y) = y + a2 ,
    uy (x, 0) = 1, u(x, b) = x2 + b.

32. ∆u(x, y) = 4 + 6y,
    ux (0, y) = 2, u(a, y) = 2y 2 + y 3 + a,
    uy (x, 0) = 0, u(x, b) = x + 2b2 + b3 .

33. ∆u(x, y) = 2,
    u(0, y) = 1 + 2y + y 2 , ux (a, y) = 0,
    u(x, 0) = 1, uy (x, b) = 1 + 2b.

34. ∆u(x, y) = 4 + 6x,
    u(0, y) = 2, ux (a, y) = 2 + 4a + 3a2 ,
    u(x, 0) = 2 + x + 2x2 + x3 , uy (x, b) = 0.

35. ∆u(x, y) = 2,
    ux (0, y) = 1, u(a, y) = 1 + y + a2 ,
    u(x, 0) = 1 + x2 , uy (x, b) = 0.

36. ∆u(x, y) = 2 + 6y,
    ux (0, y) = 2y, u(a, y) = 3 + y 2 + y 3 ,
    u(x, 0) = 3, uy (x, b) = 1 + 2b + 3b2 .

37. ∆u(x, y) = 2 + 12x2 ,
    u(0, y) = 1, ux (a, y) = 3y + 2a + 4a3 ,
    uy (x, 0) = 2, u(x, b) = 1 + x2 + x4 .

38. ∆u(x, y) = 2,
    u(0, y) = 1, ux (a, y) = 1 + 2a,
    uy (x, 0) = 0, u(x, b) = 1 + 3x + x2 .




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