Индивидуальное задание по дифурам и сду

№ Варианта	№ задания
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
1	1, 2, 3	1, 2, 3	1	1,2, 3,4	1	1	1	1	1,2	1	1	1	1	1 2 3	1 2
2	4, 5, 6	4, 5, 6	2	4,5, 6,7	2	2	2	2	3,4	2	2	2	2	4 5 6	3 4
3	7, 8, 9	7, 8, 9	3	7,8, 9,10	3	3	3	3	5,6	3	3	3	3	7 8 9	5 6
4	10, 11, 12,	10, 11, 12	4	10,11 12,13	4	4	4	4	7,8	4	4	4	4	10 11 12	7 8
5	13, 14, 15	13, 14, 15	5	13,14 15,16	5	5	5	5	9, 10	5	5	5	5	13 14 15	9 10
6	16, 17 18	16, 17 18	6	16,17 18,19	6	6	6	6	11, 12	6	6	6	6	16 17 18	11 12
7	19, 20 21	19, 20 21	7	19,20 21,22	7	7	7	7	13, 14	7	7	7	7	19 20 21	13 14
8	22, 23 24	22, 23 24	8	22,23 24,25	8	8	8	8	15, 16	8	8	8	8	22 23 24	15 16
9	25, 26 27	25, 26 27	9	25,26 27,28	9	9	9	9	17, 18	9	9	9	9	25 26 27	17 18
10	28, 29 30	28, 29 30	10	28,29 30,31	10	10	10	10	19, 20	10	10	10	10	28 29 30	19 20
1N N=1–9	N+2N+3 N+4	N+2N+3 N+4	N+3	N+2 N+3 N+4 N+5	N+3	N	N+3	N+6	N+1N+2	N	N+1	N+4	N+3	N N+10 N+14	N+1 N+9
2N N=0–9	N+5 N+6 N+7	N+5 N+6 N+7	N+6	N+6, N+7, N+8, N+9	N+6	N+1	N+7	N+4	N+6 N+11	N+1	N+3	N+1	N+4	N+1 N+17 N+12	N+8 N+11
3N N=0–9	N+7 N+8 N+9	N+6 N+7 N+8	N+4	N+1, N+2, N+9, N+10	N+4	N+7	N+4	N+1	N+4N+9	N+2	N+2	N+3	N+1	N+2 N+13 N+21	N+4 N+10

Например, задачи варианта № 16 указаны в строке 1NприN= 6, задачи варианта 23 – в строке 2NприN=3, варианта 37 – в строке 3NприN=7, и т.д.

Задание 1

Найти общее решение дифференциального уравнения:

1. sec²x^.tgy+sec²y^.tgx^.y= 0 (tgxtgy=C)

2. , (у = x sinln|Cx| )

3. y – aу = e^bx, a, b – const,

4. tgy – y xlnx = 0 ( y = arcsinCln|x|)

5. (х – у)dx +(x+y)dy = 0 ()

6. xy – y = x²cosx (y = xsinx +Cx)

7. lncos y^.dx +xtgy dy= 0 (x = Cln|cosy| )

8. ху = у + х ( +ln|Cx| = 0 )

9. (x+1)y– 3y = (x+1)⁴e^x ( y = (e^x +C)(x+1)³ )

10. 5e^xtgy = y (e^x –1)sec²y ( y=arctgC(e^x – 1)⁵ )

11. xdy =

12. y – y cosecx = tg(y = tg(x + C) )

13.

14. (y² – xy)dx + x²dy = 0 (ln|Cx| =)

15. y sinx – ycosx = 2xsin²x ( y = (x² + C)sinx )

16.

17. (x+y)y = x ()

18. (x²+1)y + 4xy = 3

19. (ху²+х) + (у–х²у)у =0 (y²+ 1 =C|x²– 1| )

20. (y = –xln|x| + Cx)

21. y + ycosx = 0,5sin2x ( y = sinx – 1 +Ce^–sinx )

22.

23.

24. ycosx – ysinx = sin2x

25. (xy² + y²) – (x²y – x²)y = 0

26. xy – y =

27. y cosx +y sinx = 1 ( y= sinx + Ccosx )

28. (1+y²)(e^2xdx –e^ydy) – (1+y)dy = 0 ( 0,5e^2x – e^y–arctgy –0,5ln(1+y²) = C )

29.

30. y(xcosy + asin2y) = 1 ( x =–2a(siny +1) +Ce^siny )