Задание

Вариант

Функция

Вариант

Функция

1

16

2

17

3

18

4

19

5

20

6

21

7

22

8

23

9

24

10

25

11

26

12

27

13

28

14

29

15

30

вариант

вариант

вариант

1

sin; x = π

11

ch; x = 2,2

21

e; x = 0,5

2

cos; x = π/2

12

sh; x = 2,8

22

arcctgh; x = 1,5

3

tg; x = 2

13

tgh; x = 0,7

23

arcsinh; x = 0,8

4

ctg; x = 2,5

14

ctgh; x = 0,8

24

arccosh; x = 1,2

5

ln; x = 3

15

sec; x = 0,5

25

arctgh; x = 1,5

6

sin²; x = 2,5

16

csc; x = 1,5

26

e²; x = 0,8

7

cos²; x = 3π/2

17

arcctg; x = 0,3

27

arcsech; x = 1,8

8

tg²; x = 0,6

18

arcsin; x = 1,5

28

arccsch; x = 1,2

9

ctg²; x = 0,8

19

arccos; x = 0,2

29

arcsec; x = 1,7

10

ln²; x = 2,7

20

arctg; x = 0,1

30

arccsc; x = 1,3

вариант

вариант

1

16

2

17

3

18

4

19

5

20

6

21

7

22

8

23

9

24

10

25

11

26

12

27

13

28

14

29

15

30

вариант

вариант

1

xy' – y = x² cos x

16

y' + 2y/x = 3x² y^4/3

2

y' + 2xy = xe^-x

17

4xy’ + 3y = -e^xx⁴y⁵

3

y' cos x + y = 1 – sin x

18

y' + y = e^x/2y^1/2

4

(1 + x²) y’ + y = arctg x

19

y' – 2y tg x + y² sin²x = 0

5

y' sin x – y cos x = 1

20

(y² + 2y + x²) y’ + 2x = 0

6

y' (x + y²) = y

21

xy' + y’ ln y = y

7

y' + 3y tg 3x = sin 6x

22

(x² ln y – x) y’ = y

8

(y⁴ + 2x) y’ = y

23

xy' – y = x² cos x

9

y' + 2y/x = 3x² y^4/3

24

y' + 2xy = xe^-x

10

4xy’ + 3y = -e^xx⁴y⁵

25

y' cos x + y = 1 – sin x

11

y' + y = e^x/2y^1/2

26

(1 + x²) y’ + y = arctg x

12

y' – 2y tg x + y² sin²x = 0

27

y' sin x – y cos x = 1

13

(y² + 2y + x²) y’ + 2x = 0

28

y' (x + y²) = y

14

xy' + y’ ln y = y

29

y' + 3y tg 3x = sin 6x

15

(x² ln y – x) y’ = y

30

(y⁴ + 2x) y’ = y

Вариант

Вариант

1

y” + xy’ + y = 0

16

y” – 4y’ + 3y = e^5x

2

y” – xy’ – 2y = 0

17

y” – 8y’ + 169y = e^4x

3

y” + x²y = 0

18

y” – 6y’ + 25y = 2 sin x + 3 cos x

4

x²y” – xy’ + 2y = 0

19

y” + y’ = cos x

5

x²y” – 3xy’ + 3y = 3 ln²x

20

y” – 6y’ + 8y = 3x² + 2x + 1

6

x²y” + xy’ + y = 1/x

21

2y” – y’ = 1

7

x²y” – 3xy’ + 3y = x³/2

22

y” + 4y’ = sin (2x + 1)

8

x²y” – xy’ + y = 0

23

y” – 4y’ = 2 sh 2x

9

y” – xy’ + y = cos ln x

24

y” + 4y’ = cos 2x

10

y” + 4y = ctg 2x

25

y” – 3y’ – 10y = xe^-2x

11

y” + 5y’ + 6y = 1/(1 + e^2x)

26

y” – y = x cos²x

12

y”cos(x/2) + (1/4) y cos(x/2) = 1

27

y” – 9y’ + 20y = x²e^4x

13

y” – 2y’ + 2y = e^x sin x

28

y” – y = 2 sh x

14

y” + 9y = 2 sin x sin 2x

29

y” – 4y = 2 ch 2x

15

y” – 4y + 8y = 61 e^2x sin x

30

y” + y = tg x

вариант

Функция

Начальные условия

Значе-ние х

Интервал

1

x’ = e^-t + y; y’ = e^t – x

x(0) = 1; y(0) = 2

x = 0,2

–3 … 3

2

x’ = 2x + y; y’ = -x + 3 sin t + t

x(0) = 0; y(0) = 1

x = 0,9

–7 … 2

3

x’ = e^3t – y; y’ = 2x + 3y + t

x(0) = 1; y(0) = 2

x = 0,2

–3 … 1

4

x’ = t + y; y’ = x + e^t

x(0) = 1; y(0) = 4

x = 1,5

–3 … 2

5

x’ = 2 sin t + y; y’ = -x + sin t

x(0) = 0; y(0) = 0

x = 1,9

–20 … 20

6

x’ = x/(x + y); y’ = y/(x + y)

x(0) = 2; y(0) = 4

x = 1

–1 … 1

7

x’ = 2x + y; y’ = -x + 2 sin t

x(0) = 1; y(0) = 0

x = 1,8

–10 … 2

8

x’ + y’ = 2(x + y); y’ = 3x + y

x(0) = 1; y(0) = 2

x = 0,8

–2 … 1

9

x’ = e^-t + sin t; y’ = e^t – x

x(0) = 1; y(0) = 4

x = 1,8

–4 … 4

10

x’ = x² + xy; y’ = xy + x²

x(0) = 1; y(0) = 0

x = 0,5

–1 … 0,5

11

x’ = e^2t – 3y; y’ = 2x + y

x(0) = 1; y(0) = 4

x = 0,2

–10 … 2

12

x’ = 2 cos t + y; y’ = -x + 2y

x(0) = 1; y(0) = 1

x = 1,8

–3 … 2

13

x’ = t – у; y’ = е^2t + х

x(0) = 1; y(0) = 4

x = 1,5

–10 … 2

14

x’ = 2x – 5y; y’ = x + y

x(0) = 1; y(0) = 1

x = 3

–2 … 1

15

x’ = 8x – y; y’ = x + y

x(0) = 1; y(0) = 4

x = 0,5

–2 … 0,8

16

x’ + 2x =1; y’= y + 3x – 1

x(0) = 1; y(0) = 0

x = 1,4

–2 … 2

17

x’ = e^-t – 5y; y’ = 2x – 3y

x(0) = -1; y(0) = 2

x = 2

–2 … 3

18

x’ = 12x – 5y; y’ = 5x + 12y

x(0) = 1; y(0) = 0

x = 0,3

0 … 0,7

19

x’ = 3t + 5y; y’ = 2x + e^t

x(0) = 1; y(0) = 2

x = 1

–1 … 1

20

x’ = x – 4y; y’ = x + y

x(0) = 1; y(0) = 0

x = 1,8

–1 … 6,5

21

x’ = e^-5t – 2y; y’ = e^t – 3x

x(0) = 1; y(0) = 2

x = 0,2

–1 … 1

22

x’ = 2x – 3y; y’ = 5x + 2y

x(0) = -1; y(0) = 2

x = 1

–2 … 0,5

23

x’ = 8x – 3y; y’ = 5x + y

x(0) = 0; y(0) = 2

x = 0,5

–1 … 0,5

24

x’ + 2x =1 + у; y’= 2x – 1

x(0) = 0; y(0) = 2

x = 0,7

0 … 1

25

x’ = e^-3t – 2y; y’ = x – 3y +1

x(0) = -1; y(0) = 4

x = 1,7

0 … 5

26

x’ = x – y; y’ = x – 3y + 1

x(0) = -1; y(0) = 4

x = 1,2

–1 … 5

27

x’ = x – 2y; y’ = 5x – 3y + 1

x(0) = -1; y(0) = 2

x = 0,9

–2 … 5

28

x’ = 4x + 6y; y’ = 2x + 3y + t

x(0) = 0; y(0) = -1

x = 0,1

–7 … 0,5

29

x’ = 3x + y; y’ = -4x – y

x(0) = 3; y(0) = 0

x = 0,2

–7 … 1

30

x’ = 2x + y; y’ = x + 2y

x(0) = 1; y(0) = 3

x = 0,1

–2 … 1

вариант

Функция

Начальные условия

Интервал

1

x’ = e^-t + y; y’ = e^t – x

x(0) = 1; y(0) = 1

–3 … 2

2

x’ = 8x – y; y’ = cos t + y

x(0) = 1; y(0) = 2

–10 … 0

3

x’ = cos 3t + y; y’ = -4x – y

x(0) = 1; y(0) = 2

–5 … 2

4

x’ = t + y cos t; y’ = x + e^t

x(0) = 1; y(0) = 0

–12 … 5

5

x’ + 2x/t =1; y’= x sin t – y

x(0) = 0; y(0) = 1

–12 … 2

6

x’ = 2x – cos t; y’ = x – y

x(0) = 0; y(0) = 1

–3 …–2

7

x’ = sin t – 5y; y’ = 5x + 12y

x(0) = 0; y(0) = 0

–7 … 0,5

8

x’ = x – 4y; y’ = sin t + t

x(0) = 1; y(0) = 0

–4 … 2

9

x’ + y’ = 2y sin t; y’ = 3x + y

x(0) = 1; y(0) = 1

–3 … 3

10

x’ = 4x cos t + 6y; y’ = 3y + t

x(0) = 1; y(0) = 0

–3 … 2

11

x’ = x² + xy; y’ = sin t + x²

x(0) = 1; y(0) = 1

–5 … 0,4

12

x’ = 2x sin t + t; y’ = x + y

x(0) = 1; y(0) = 3

–8 … 3

13

x’ = sin t /(x + y); y’ = y/(x + y)

x(0) = 2; y(0) = 4

–5 … 5

14

x’ = x + 2y; y’ = -x + 2 sin t

x(0) = 1; y(0) = 0

–5 … 5

15

x’ = e^3t – y; y’ = 2x sin t + t

x(0) = 1; y(0) = 1

–7 … 2

16

x’ = 3x – y; y’ = 2cos t + 3y

x(0) = 1; y(0) = 2

–3 … 1

17

x’ = xy – 2y²; y’ = xy

x(0) = 1; y(0) = 2

–5 … 1

18

x’ = e^5t – 2y; y’ = x cos t + t

x(0) = 0; y(0) = 2

–7 … 1,5

19

x’ = 3x sin 2t + y; y’ = 3y + t

x(0) = 1; y(0) = 0

–5 … 1

20

x’ = 3xy + y; y’ = 3y + t

x(0) = 0; y(0) = 2

–5 … 0,2

21

x’ = sin 2t + 3y; y’ = -cos t + 2x

x(0) = 0; y(0) = 2

–2 … 2

22

x’ = 2xy – y; y’ = 3x + t

x(0) = 1; y(0) = 2

–5 … 0,4

23

x’ = 3x sin t + y; y’ = x/y

x(0) = 2; y(0) = 2

–2 … 1

24

x’ = cos 2t + y; y’ = -cos t + 3y

x(0) = 1; y(0) = 2

–7 … 0,5

25

x’ = xy – 2y; y’ = 3x + y

x(0) = 1; y(0) = 2

–5 … 1

26

x’ = 2y sin t + y; y’ = x/y

x(0) = 2; y(0) = 2

–3 … 2

27

x’ = 2y e^t + y; y’ = x/y

x(0) = 0; y(0) = 2

–3 … 2

28

x’ = xy – 2x²; y’ = 2xy

x(0) = 1; y(0) = 2

–0.7 … 0.3

29

x’ = 3x sin t + y²; y’ = xy

x(0) = 1; y(0) = 2

–1 … 0,5

30

x’ = 2xy e^2t + y; y’ = 5x/y

x(0) = -1; y(0) = 2

–5 … 0,5

вар

Функция

Интервал по t

Цвет линий

Цвет стрелок

1

x’ = y; y’ = -x –у

0 …2π

tan

cyan

2

x’ = x + y; y’ = – 2xу

-0,5 … 0,5

violet

coral

3

x’ = ; y’ = -x

0 …2π

blue

red

4

x’ = x² + y; y’ = –xу

–0,15 … 0,15

yellow

blue

5

x’ = y; y’ = 2xу

–0,3 … 0,3

navy

grey

6

x’ = 2y; y’ = 3x/y

0 …1

cyan

green

7

x’ = 2y; y’ = -4x – y

–0,5 … 0,5

blue

green

8

x’ = x²; y’ = xу

0 …0,1

green

red

9

x’ = x + y; y’ = – 2xу

–1 … 1

maroon

plum

10

x’ = 2xy; y’ = x/у

0 …0,2

cyan

magenta

11

x’ = ; y’ = xy

–1 … 0,5

khaki

coral

12

x’ = 4x + 3y; y’ = 3y

0 …0,5

red

orange

13

x’ = ; y’ = -x

0 …2π

orange

yellow

14

x’ = 8x – y; y’ = 5y

–0,2 … 0,2

brown

black

15

x’ = 3y; y’ = -2x – 5y

–0,4 … 0,4

pink

gold

16

x’ = у + х; y’= -x

0 …2π

cyan

tan

17

x’ = 2x; y’ =

0 …0,5

coral

violet

18

x’ = 4y; y’ = 3x/2y

–0,3 …0,3

red

blue

19

x’ = 4хy; y’ = 1/2y

–0,2 …0,2

blue

yellow

20

x’ = у²; y’ = xу

–0,3 …0,3

grey

navy

21

x’ = х/y; y’ = x – y

–0,1 … 0,1

green

cyan

22

x’ = x² – y; y’ = x/у

–0,15 … 0,15

gold

pink

23

x’ = ; y’ = x – y

–0,5 … 0,5

red

green

24

x’ = хy + у; y’ = -x – 2y

–0,2 … 0,2

plum

maroon

25

x’ = ; y’ = y + хy

0 …0,4

magenta

cyan

26

x’ = x²; y’ = x – у²

–0,1 … 0,1

coral

khaki

27

x’ = 2хy; y’ = 1/2х

–0,3 …0,3

orange

red

28

x’ = 3x – 2y; y’ = 5y

–0,4 … 0,4

yellow

orange

29

x’ = 2х + y; y’ = 1/2хy

–0,4 …0,4

black

brown

30

x’ = х/y; y’ = -x – 2y

–0,1 … 0,1

green

blue

вариант

Функция

Интервал по х

Интервал по у

Цвет линий

Цвет стрелок

1

x’ = у² + х; y’ =

0 …40

–5 … 10

green

blue

2

x’ = у² + 3ху; y’ =

–40 …40

–5 … 7

red

green

3

x’ = у² + х³; y’ = 2x – 5y

–10 …10

–20 … 20

plum

maroon

4

x’ = у² + х; y’ = 2x^,3 – y

–10 …10

–20 … 20

magenta

cyan

5

x’ = 2у² + ху; y’ = x – хy

–10 …20

–7 … 7

coral

khaki

6

x’ = 2y; y’ = 3x + y

–10 …10

–10 … 10

orange

red

7

x’ = 4x + 6y; y’ = 3y + х

–20 …20

–15 … 15

yellow

orange

8

x’ = x² + xy; y’ = x

–10 …20

–15 … 5

black

brown

9

x’ = 2xу; y’ = x + y

–10 …20

–5 … 8

gold

pink

10

x’ = х² ; y’ = y + хy

–10 …10

–20 … 20

tan

cyan

11

x’ = x + 2y; y’ = -x² + у²

–20 …10

–20 … 20

violet

coral

12

x’ = y²; y’ = 2x + у²

–10 …10

–15 … 15

blue

red

13

x’ = x + y; y’ = –x³

–7 …7

–10 … 10

yellow

blue

14

x’ = 8x – y; y’ = y³

–10 …10

–5 … 5

navy

grey

15

x’ = ху² + y; y’ = -4x – y

–20 …20

–7 … 7

cyan

green

16

x’ = ху³; y’ = -x – 2y

–20 …40

–7 … 7

blue

green

17

x’ = у² + y; y’ = -x – х²

–10 …10

–10 … 10

green

red

18

x’ = х² + y; y’ = у – х²

–10 …10

–20 … 10

maroon

plum

19

x’ = х² + 2хy; y’ = у – 3х

–20 …20

–10 … 10

cyan

magenta

20

x’ = у² + y³; y’ = x – y

–20 …20

–7 … 7

khaki

coral

21

x’ = у² + х³; y’ = 2x – y

–5 …5

–5 … 10

red

orange

22

x’ = у² + ; y’ = 2x + y

0 …20

–5 … 10

orange

yellow

23

x’ =3х²; y’ = 2x – у²

–10 … 10

–10 … 10

brown

black

24

x’ =3х² – у; y’ = x + у²

–5 … 5

–20 … 20

pink

gold

25

x’ = 2x; y’ = x – y

–25 …25

–20 …20

cyan

tan

26

x’ = 5y; y’ = 5x + 12y

–25 … 25

–40 … 40

coral

violet

27

x’ = 5y; y’ =

–10 … 10

0 … 8

red

blue

28

x’ = 3ху² + 1; y’ = x – 2y

–20 …20

–5 … 7

blue

yellow

29

x’ = ху² + ; y’ =

0 …20

0 … 6

grey

navy

30

x’ = у² + 5ху; y’ = x – y³

–20 …20

–5 … 3

green

cyan