Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 24 стр.

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15. ∆u(x, y) = 2,
u(0, y) = 1 − b + y + y
2
, u(a, y) = 1 + a + y
2
,
u
y
(x, 0) = 1, u(x, b) = 1 + x + b
2
.
16. ∆u(x, y) = 2,
u(0, y) = 1 + y
2
, u(a, y) = 1 + a − b + y + y
2
,
u
y
(x, 0) = 2x, u(x, b) = 1 + x + b
2
.
17. ∆u(x, y) = 2,
u(0, y) = 1 − 2b + 2y, u(a, y) = 1 + a + a
2
,
u
y
(x, 0) = 1, u(x, b) = 1 + x + x
2
.
18. ∆u(x, y) = 2,
u(0, y) = 1, u(a, y) = 1 + a + a
2
− b + y,
u
y
(x, 0) = x, u(x, b) = 1 + x + x
2
.
19. ∆u(x, y) = 2,
u(0, y) = y
2
, u(a, y) = 1 + y
2
,
u
y
(x, 0) = 2, u
y
(x, b) = 2b.
20. ∆u(x, y) = 4,
u(0, y) = y + 2y
2
, u(a, y) = 1 + 2y
2
,
u
y
(x, 0) = 0, u
y
(x, b) = 2.
21. ∆u(x, y) = 2 + 6y,
u(0, y) = 2y + y
2
+ y
3
, u(a, y) = y
2
+ y
3
,
u
y
(x, 0) = 0, u
y
(x, b) = 2x + 2b + 3b
2
.
22. ∆u(x, y) = 4 + 12y
2
,
u(0, y) = 2y
2
+ y
4
, u(a, y) = 3y + 2y
2
+ y
4
,
u
y
(x, 0) = 1, u
y
(x, b) = 4b + 4b
3
.
23. ∆u(x, y) = 4,
u
x
(0, y) = 1, u
x
(a, y) = 4a,
u(x, 0) = 2x
2
, u(x, b) = x + 2x
2
.
24. ∆u(x, y) = 2,
u
x
(0, y) = 0, u
x
(a, y) = 3y + 2a,
u(x, 0) = 2x + x
2
, u(x, b) = x
2
.
25. ∆u(x, y) = 4 + 6x,
u
x
(0, y) = 2, u
x
(a, y) = 4a + 3a
2
,
u(x, 0) = 2x
2
+ x
3
, u(x, b) = 3 + 2x
2
+ x
3
.
26. ∆u(x, y) = 2 + 12x
2
,
u
x
(0, y) = 0, u
x
(a, y) = y + 2a + 4a
3
,
u(x, 0) = 1 + x
2
+ x
4
, u(x, b) = x
2
+ x
4
.
24
15. ∆u(x, y) = 2,
    u(0, y) = 1 − b + y + y 2 , u(a, y) = 1 + a + y 2 ,
    uy (x, 0) = 1, u(x, b) = 1 + x + b2 .

16. ∆u(x, y) = 2,
    u(0, y) = 1 + y 2 , u(a, y) = 1 + a − b + y + y 2 ,
    uy (x, 0) = 2x, u(x, b) = 1 + x + b2 .

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

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

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

20. ∆u(x, y) = 4,
    u(0, y) = y + 2y 2 , u(a, y) = 1 + 2y 2 ,
    uy (x, 0) = 0, uy (x, b) = 2.

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

22. ∆u(x, y) = 4 + 12y 2 ,
    u(0, y) = 2y 2 + y 4 , u(a, y) = 3y + 2y 2 + y 4 ,
    uy (x, 0) = 1, uy (x, b) = 4b + 4b3 .

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

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

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

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




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