Приложение а

№

Уравнение

t₀

t_f

y₀

y'₀

Точное решение

1

2

3

4

5

6

7

1

y"–y= –2(sint+cost)

0

10

1

1

cost+sint

2

(1+t²)y"+y'²+1= 0

0

10

1

1

1–t +2ln(1+t)

3

y"+2y'+2y=2e^–tcost

0

10

1

0

e^–t (cost+sint+t sint)

4

y"+4y = e^3t (13t– 7)

0

4

0

-4

cos2t–sin2t+e^3t (t–1)

5

y"+4y'+4y = e^t

0

10

1

-1

(8/9+2/3t)e^–2t+1/9e^t

6

y"–y = sint+cos2t

0

10

1,8

-0,5

e^t+e^–t–0,5sint–0,2cos2t

7

y"+4y = cos3t

0

10

0,8

2

cos2t+sin2t–0,2cos3t

8

y"–2y'+y = 5te^t

0

5

1

2

e^t(1+t+5t³/6)

9

y"+y'–6y = 3t²–t–1

0

5

-0,9

3,2

0,1e^2t–e^–3t–0,5 t²

10

8y"+2y'–3y = t +5

0

20

1/9

-7/12

e^t/2+e^–3t/4–t/3–17/9

11

t²y"–2y = 0

1

30

5/6

2/3

1/2t²+1/3t^–1

12

y"–4y'+5y = 3t

0

5

1,48

3,6

e^2t (cost+sint)+0,6t+0,48

13

y"–3y'+2y = t²+3t

0

6

5,1

4,2

e^t+0,1e^2t+t²/2+3t+4

14

y"+ y = 1+e^t

0

11

2,5

1,5

cost+sint+e^t/2+1

15

t²y"+t y'–y = 8t³

1

30

4

4

t³+2t+t^–1

16

t²y"+ty' = 0

1

30

5

-1

5-lnt

17

y"–2y'+y = te^t

0

6

1

2

e^t(t³/6+t+1)

18

t²y"+2,5ty'–y = 0

1

30

2

3,5

3t^0,5– t^–2

19

4ty"+2y'+y=0

1

10²

1,38177

-0,15058

sin t^0,5+cos t^0,5

20

t²y"–4ty'+6y = 2

1

11

43/30

2,3

0,1t³+t²+1/3

21

y"- y = e^2t (t–1)

0

5

11/9

-11/9

e^t+e^–t+e^2t (1/3t–7/9)

22

2y"–y'– y = 6e^t/2

0

10

-4

-2,5

e^t- 6e^t/2+e^–t/2

23

y"+4y'+4y = 2t–3

0

10

-1/4

-1/2

(1+t)e^–2t+t/2- 5/4

24

y"+y = t²–t+2

0

20

1

0

cost+sint+t²- t

25

y"+4y=sint+sin2t

0

20

1

-23/12

(1-t/4)cos2t-sin2t+1/3sint

26

t²y"+y'-2y=t–t^–2/3–7

1

30

26/6

2/3

t²/2+t ^–1/3+3,5

27

t²y"+6y=8t²+1,2t³

1

11

1,1

2,3

(0,1t+1) t²

28

y"+y' =2t–2sint–3

0

20

8

-4

cost+sint+t²–5t +7

29

y"+t^–1y'=9t+5t^–1+t^–3

1

30

13

7

t³+5t+t^–1+6

30

t²y"+2y=11–2lnt+4t

1

30

7

1

5–lnt+2t