Вычислительная Математика / Job-13

0.951.00

Y

0.90

0.85

0.80

Точныезначения

0.75

Эйлерn=5

0.70

Эйлерn=10

0.65

мод. Эйлерn=5

0.60

мод. Эйлерn=10

0.55

X

0.50

0

0.08

0.16

0.24

0.32

0.4

0.48

0.56

0.64

0.72

0.8

y |x=1 =0

1

1

1

x2 y′−1 = xy

1 ≤ x ≤ 2

yтеор =

x −

2

x

2

yy′+ 2x = y 2

y |x=0 =1

0 ≤ x ≤1

yтеор

=

2x +1

3

xy′−3y = x2

y |x=1 =0

1 ≤ x ≤ 2

yтеор

= x2 (x −1)

4

y

′

= xy

y |x=0 =1

0 ≤ x ≤1

yтеор

x2

= e 2

5

x2 y′− y 2

= xy

y |x=1 =1

1 ≤ x ≤ 2

yтеор

=

x

1 −ln x

6

xy′+ y −1 = ln x

y |x=1 =0

1 ≤ x ≤ 2

yтеор

= ln x

7

xy′− x = y

y |x=1 =0

1 ≤ x ≤ 2

yтеор

= x ln x

8

y′+ 2xy = xe-x2

y |x=0 =0

0 ≤ x ≤1

yтеор

=

1

x2

e−x2

2

9

y′+ y cos x =

1

sin 2x

y |x=0 =0

0 ≤ x ≤1

yтеор = sin x +e−sin x −1

2

10

y′+ y tg x = sin 2x

y |x=0 = −1

0 ≤ x ≤1

yтеор = (1 −2 cos x)cos x

11

xy′− y 2 ln x + y = 0

y |x=1 =1

1 ≤ x ≤ 2

yтеор

=

1

1 +ln x

12

xy′ = x + y + x e y x

y |x=1 =0

1 ≤ x ≤1.9

yтеор = x ln

x

2 − x

13

x2 y′− y = x2 e

x−1

y |x=1 =1

1 ≤ x ≤ 2

yтеор

= e

x2 −1

x

x

14

(x2 +1)y′+ xy =1

y |x=0 =0

0 ≤ x ≤1

yтеор = ln(x +

x2

+1)

x2

+1

15

xy′− y =

x

y |x=e = 0

e ≤ x ≤ e +1

yтеор

= x ln ln x

ln x

16

xy′− y = x2 sin x

y |x=

π = 0

π

≤ x ≤

π

+1

yтеор

= −x cos x

2

2

2

17

xy′+ y = x sin x

y |x=

π = 0

π

≤ x ≤

π

+1

yтеор =

sin(x)−1

−cos x

2

2

2

x

18

y′+e x−y

= e x(1−x )+2x

y |x=0 =0

0 ≤ x ≤1

yтеор

= x2

19

xy′ = y ln y

y |x=1 =e

1 ≤ x ≤ 2

yтеор

= e x

20

xy′− y(ln(xy)−1)= 0

y |x=1 =e

1 ≤ x ≤ 2

yтеор

=

e x

x

21

xy′ = x sin

y

+ y

y |x=1 =

π

1 ≤ x ≤ 2

yтеор = 2x arctg x

x

2

22

x2 y′ = (x −1)y

y |x=1 =e

1 ≤ x ≤ 2

1

yтеор

= x e

x

23

(x2 +1)y′+ xy = x(x2 +1)

y |x=

2 =1

2 ≤ x ≤

2 +1

yтеор

=

x2

+1

3

24

y′−

y

= x ln x

y |x=e =

e2

e ≤ x ≤ e +1

yтеор

=

x2

ln x

x ln x

2

2

y′− y ctg x = sin x

y |x=

π = 0

π

π

π

25

≤ x ≤

+1

yтеор =

x

−

sin x

2

2

2

2

26

x + y

−1 = 0

y |x =0 =1

0 ≤ x ≤1

yтеор = 2 ex − x −1

y'

27

(1

+

x

2

) y'

−

(1

+

y

2

)

=

0

y |

x=2

= −3

2

≤

x

≤

3

y

теор

=

1 + x

1 − x

28

x( y2 +1) + yy'(1 −x2 ) = 0

y |x =1,5 =1,5

1.5 ≤ x ≤ 2.5

yтеор =

−2.6(1 − x2 ) −1

29

xyy'=1 − x2

y |x =0.5 =1.3

0.5 ≤ x ≤1.5

y

теор

=

ln(27.835) +ln(x2 ) − x2

30

y' y2 + 2x =1

y |x =0 =1

0 ≤ x ≤1

yтеор

= 3

3x(1 − x) +1

31

y' x + y = y2

y |x =1 = 0.5

1 ≤ x ≤ 2

yтеор =

1

1 + x

32

1

y'=1

y |x =2.5 = −2.8656

2.5 ≤ x ≤3.0

y

теор

= −ln(1050 −10x )

10( x +y)

ln(10)