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

1. 18

2. .1

3. 18.2

4. 18.3

5. 18.4

6. 18.5

7. 18.6

8. 18.7

9. 18.8

10. 18.9 ydx – (x+y)dy = 0

11. 18.10(y²-3x²)dx – 2xydy = 0

12. 18.11 (x²+2xy-y²)dx+(y²+2xy-x²)dy = 0

13. _18.12

14. 18.13 (y²-2xy)dx+x²dy = 0

15. 18.14 y²+x²y^| = xyy^|

16. 18.15(x²+y²)y^| = 2xy

17. 18.16 xy^|-y=x

18. _18.17

19. 18.18

20. 18.19

21. _18.20

1. xy^|+y = y² ln x

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

3. x² dy = (2xy+x²-y)dx

4. 2x (x²+y) dx = dy

5. xy^|+(x+1)y = 3x²e^-x

6. (x+y²)dy = ydx

7. (sin²y+x ctgy) y^| = 1

8. (2x+y) dy = ydx+4 lny dy

9. xy dy = (y²+x) dx

10. y^| x³ siny = xy^|-2y

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

12. y = x (y^|-x cosx)

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

14. 2e^y-xy^| = 1

15. xy²y^| = x²+y³

16. xy^|-2x² = 4y

17. 2y^|-=

18. (2x²y lny-x) y^| = y

19. 2xy^|-6y = -x²

20. y^|+y cosx = sinx cosx

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

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

3. yy^||+1=y^|2

4. y^||| = 2(y^||-1) ctgx

5. yy^|| = y^|2-y^|3

6. 2yy^|| = y²+y^|2

7. y^||2+y^| = xy^||

8. y^||+y^|2=2e^-y

9. y^||2 = y^|2+1

10. 2y^| (y^||+2) = xy^||2

11. y^|2 = (3y-2y^|) y^||

12. y^|| (2y^|+x) = 1

13. (1-x²) y^||+xy^| = 2

14. yy^||-2yy^| lny = y^|2

15. (y^|+2y) y^|| = y^|2

16. xy^|| = y^|+x

17. yy^||+y = y^|2

18. 2yy^|3+y^|| = 0

19. y^|| (3y+4) – 3y^|2 = 0

20. 2xy^|y^|| = y^|2+1

1. a) y^||+y^|-2y = 0

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

3. a) y^||-2y = 0

4. b) y^||+2y^|-3y = x²e^x

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

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

7. a) y^||+4y = 0

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

9. a) 4y^||+4y^|+y = 0

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

11. a) y^|||-3y^||+3y^|-y = 0

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

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

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

15. a) y^||+4y^|+3y = 0

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

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

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

19. a) y^||+2y^|+10y = 0

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

21. 21.11. a) y^||-2y^|+y = 0

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

23. 21.12. a) y^|||-6y^||+9y^| = 0

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

21. 13. a) y^||+2y^|+y = 0

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

20. 14. a) y^|||-y^||-y^|+y = 0

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

13. a) y^|||+8y^||+16y^| = 0

27. b) y^||-y = 2e^x-x²

13. a) y^||+4y^|+3y = 0

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

13. a) y^||+y^|-2y = 0

29. b) y^||-5y^| = 3x²+sin5x

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

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

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

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

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

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