Контрольные работы по уравнениям математической физики. Ковтанюк А.Е. - 23 стр.

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3. ∆u(x, y) = 4 + 6x,
u(0, y) = 3y
2
, u(a, y) = 3y
2
+ a
2
+ a
3
,
u(x, 0) = x
2
+ x
3
, u(x, b) = x
2
+ x
3
+ 3b
2
.
4. ∆u(x, y) = 2 + 6y,
u(0, y) = 2y
2
+ y
3
, u(a, y) = 2y
2
+ y
3
+ 3a
2
,
u(x, 0) = 3x
2
, u(x, b) = 3x
2
+ 2b
2
+ b
3
.
5. ∆u(x, y) = 2 + 12x
2
,
u(0, y) = 3y
2
, u(a, y) = 3y
2
+ 2a
2
+ a
4
,
u(x, 0) = 2x
2
+ x
4
, u(x, b) = 2x
2
+ x
4
+ 3b
2
.
6. ∆u(x, y) = 4 + 12y
2
,
u(0, y) = y
2
+ y
4
, u(a, y) = y
2
+ y
4
+ 3a
2
,
u(x, 0) = 3x
2
, u(x, b) = 3x
2
+ b
2
+ b
4
.
7. ∆u(x, y) = 2 + 6x + 12x
2
,
u(0, y) = 2y
2
, u(a, y) = 2y
2
+ 3a
2
+ a
3
+ a
4
,
u(x, 0) = 3x
2
+ x
3
+ x
4
, u(x, b) = 3x
2
+ x
3
+ x
4
+ 2b
2
.
8. ∆u(x, y) = 4 + 6y + 12y
2
,
u(0, y) = y
2
+ y
3
+ y
4
, u(a, y) = y
2
+ y
3
+ y
4
+ a
2
,
u(x, 0) = x
2
, u(x, b) = x
2
+ b
2
+ b
3
+ b
4
.
9. ∆u(x, y) = 6 + 6y + 12x
2
,
u(0, y) = 2y
2
+ y
3
, u(a, y) = 2y
2
+ y
3
+ a
2
+ a
4
,
u(x, 0) = x
2
+ x
4
, u(x, b) = x
2
+ x
4
+ 2b
2
+ b
3
.
10. ∆u(x, y) = 2 + 6x + 12y
2
,
u(0, y) = 3y
2
+ y
4
, u(a, y) = 3y
2
+ y
4
+ 2a
2
+ a
3
,
u(x, 0) = 2x
2
+ x
3
, u(x, b) = 2x
2
+ x
3
+ 3b
2
+ b
4
.
11. ∆u(x, y) = 2,
u
x
(0, y) = 1, u(a, y) = 1 + y + y
2
,
u(x, 0) = 1 − 2a + 2x, u(x, b) = 1 + b + b
2
.
12. ∆u(x, y) = 2,
u
x
(0, y) = y, u(a, y) = 1 + 2y + a
2
,
u(x, 0) = 1 + x
2
, u(x, b) = 1 − a + 2b + x + x
2
.
13. ∆u(x, y) = 2 + 6y,
u
x
(0, y) = 3y, u(a, y) = 2 + y + y
2
+ y
3
,
u(x, 0) = 2 − a + x, u(x, b) = 2 + b + b
2
+ b
3
.
14. ∆u(x, y) = 2 + 6x,
u
x
(0, y) = 1, u(a, y) = 1 + 3y + a
2
+ a
3
,
u(x, 0) = 1 + x
2
+ x
3
, u(x, b) = 1 − 3a + 3b + 3x + x
2
+ x
3
.
23
 3. ∆u(x, y) = 4 + 6x,
    u(0, y) = 3y 2 , u(a, y) = 3y 2 + a2 + a3 ,
    u(x, 0) = x2 + x3 , u(x, b) = x2 + x3 + 3b2 .

 4. ∆u(x, y) = 2 + 6y,
    u(0, y) = 2y 2 + y 3 , u(a, y) = 2y 2 + y 3 + 3a2 ,
    u(x, 0) = 3x2 , u(x, b) = 3x2 + 2b2 + b3 .

 5. ∆u(x, y) = 2 + 12x2 ,
    u(0, y) = 3y 2 , u(a, y) = 3y 2 + 2a2 + a4 ,
    u(x, 0) = 2x2 + x4 , u(x, b) = 2x2 + x4 + 3b2 .

 6. ∆u(x, y) = 4 + 12y 2 ,
    u(0, y) = y 2 + y 4 , u(a, y) = y 2 + y 4 + 3a2 ,
    u(x, 0) = 3x2 , u(x, b) = 3x2 + b2 + b4 .

 7. ∆u(x, y) = 2 + 6x + 12x2 ,
    u(0, y) = 2y 2 , u(a, y) = 2y 2 + 3a2 + a3 + a4 ,
    u(x, 0) = 3x2 + x3 + x4 , u(x, b) = 3x2 + x3 + x4 + 2b2 .

 8. ∆u(x, y) = 4 + 6y + 12y 2 ,
    u(0, y) = y 2 + y 3 + y 4 , u(a, y) = y 2 + y 3 + y 4 + a2 ,
    u(x, 0) = x2 , u(x, b) = x2 + b2 + b3 + b4 .

 9. ∆u(x, y) = 6 + 6y + 12x2 ,
    u(0, y) = 2y 2 + y 3 , u(a, y) = 2y 2 + y 3 + a2 + a4 ,
    u(x, 0) = x2 + x4 , u(x, b) = x2 + x4 + 2b2 + b3 .

10. ∆u(x, y) = 2 + 6x + 12y 2 ,
    u(0, y) = 3y 2 + y 4 , u(a, y) = 3y 2 + y 4 + 2a2 + a3 ,
    u(x, 0) = 2x2 + x3 , u(x, b) = 2x2 + x3 + 3b2 + b4 .

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

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

13. ∆u(x, y) = 2 + 6y,
    ux (0, y) = 3y, u(a, y) = 2 + y + y 2 + y 3 ,
    u(x, 0) = 2 − a + x, u(x, b) = 2 + b + b2 + b3 .

14. ∆u(x, y) = 2 + 6x,
    ux (0, y) = 1, u(a, y) = 1 + 3y + a2 + a3 ,
    u(x, 0) = 1 + x2 + x3 , u(x, b) = 1 − 3a + 3b + 3x + x2 + x3 .




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