22.

X

6.0

6.5

7.0

7.5

6.2

Y

1.35

0.775

1.79

0.862

23.

X

5.0

5.5

6.0

6.5

5.7

Y

0.667

0.589

0.922

0.993

24.

X

6.0

6.5

7.0

7.5

7.7

Y

0.840

0.517

1.94

1.05

1

1

ln 2

e

x

1.

∫3(x2 + x ex2 )dx

2.

∫arctg

xdx

3. ∫

dx

1−e

2 x

0

0

0

e ln2 x

e3

dx

π

2

x

4.

5.

∫

∫

x2

dx.

6.

∫0

cos2

xdx

x 1+lnx

1

1

2

10

1

2

xdx

7.

∫

8.

∫

x −1

dx

9. ∫x arctgxdx.

4 − x

2

1

5

0

8

2

∫1 arctgxdx

0

dx

10. ∫(5x −10)e−2 x dx

11.

12.

∫

1

+ x +2

0

0

−1

∫1

3

e

12x5dx

14.

(x2 −1)e2x+1dx

5 (lnx +1)4

13.

∫

15.

∫

dx

x

x

6

+1

−

1

0

2

1

π

17.

12

dx

18.

1

)e

dx

2

∫

∫(1− x

2

2−x

16. ∫sin3xdx

1

4 + x

0

5

−2

19.

5

7x5dx

20.

∫2 (5− x2 )e−3x dx

21. ln∫2

ex

dx

∫

x6 +1

1−e2 x

0

0

0

2

dx

1

e3

3dx

22.

∫

23.

∫2x arctgxdx.

24.

∫

x

9x2 −16

1+lnx

−1

0

1

0.66x1 +0.44x2 +0.22x3 = −0.58

0.72x1 +3.54x2 +7.28x3 = 0.33

1. 1.54x1 +0.74x2 +1.54x3 = −0.32

2. −0.28x1 −0.72x2 +3.04x3 = 0.22

1.42x1 +1.42x2 +0.86x3 = 0.83

1.00x1 +0.35x2 −0.75x3 =1.12

0.45x1 −0.94x2 −0.15x3 = −0.15

1.02x1 −0.73x2 −9.11x3 = −1.25

3. −0.01x1 +0.34x2 +0.06x3 = 0.31

4. 6.25x1 +2.32x2 +7.62x3 = 2.32

−0.35x1 +0.05x2 +0.65x3 = 0.37

1.13x1 −8.88x2 +4.64x3 = −3.75

0.78x1 −0.02x2 −0.12x3 = 0.56

0.34x1 +0.71x2 +0.63x3 = 2.08

5. 0.02x1 −0.86x2 +0.04x3 = 0.77

6. 0.71x1 −0.65x2 −0.17x3 = 0.18

0.12x1 +0.44x2 −0.72x3 =1.01

1.18x1 −2.35x2 +0.75x3 =1.28

9

0.21x1 −0.18x2 +0.75x3 = 0.11

0.92x1 −0.83x2 +0.62x3 = 2.15

7. 0.13x1 +0.75x2 −0.11x3 = 2.01

8. 0.24x1 −0.54x2 +0.43x3 = 0.62

3.01x −0.33x

2

+0.11x = 0.13

0.73x

−0.81x

2

−0.67x = 0.88

1

3

1

3

0.63x1 +0.05x2 +0.15x3 = 0.34

0.62x1 +0.92x2 +0.03x3 = −0.82

9. 0.15x1 +0.10x2 +0.71x3 = 0.42

10.

0.99x1 +0.01x2 +0.07x3 = 0.66

−0.02x2

+0.99x3 = −0.98

0.03x1 +0.34x2 +0.10x3 = 0.32

1.01x1

−0.20x1 +1.60x2 −0.10x3 = 0.30

0.10x1 −0.07x2 −0.96x3 = −2.04

11. −0.30x1 +0.10x2 −1.50x3 = 0.40

12. 0.04x1 −0.99x2 −0.85x3 = −3.73

−0.20x2

+0.30x3 = −0.60

+1.04x2

+0.19x3 = −1.67

1.20x1

0.91x1

0.30x1 +1.20x2 −0.20x3 = −0.60

0.62x1 +0.84x2 +0.77x3 = −8.18

13. −0.10x1 −0.20x2 +1.60x3 = 0.30

14. 0.03x1 −1.11x2 −1.08x3 = 0.08

0.50x

+0.34x

2

+0.10x = 0.32

0.97x

+0.02x

2

−1.08x = 0.06

1

3

1

3

0.13x1 −0.14x2 −2.00x3 = 0.15

0.21x1 −0.94x2 −0.94x3 = −0.25

15.

0.75x1 +0.18x2 +0.77x3 = 0.11

16. 0.98x1 −0.19x2 +0.93x3 = 0.23

0.28x −0.17x

2

+0.39x = 0.12

0.87x +0.56x

2

−0.14x = 0.33

1

3

1

3

0.98x1 +0.88x2 −0.24x3 =1.36

0.20x1 +0.44x2 +0.81x3 = 0.74

17. 0.16x1 −0.44x2 −0.88x3 = −1.27

18.

0.58x1 +0.29x2 +0.05x3 = 0.02

9.74x

−10x

2

+

1.74x = −5.31

0.05x

+0.34x

2

+0.10x = 0.32

1

3

1

3

0.20x1 +0.44x2 +0.81x3 = 0.74

0.63x1 −0.37x2 +1.76x3 = −9.29

19.

0.58x1 +0.29x2 +0.05x3 = 0.02

20. 0.90x1 +0.99x2 +0.05x3 = 0.12

0.05x +0.34x

2

+0.10x = 0.32

0.13x −0.95x

2

+0.69x = 0.69

1

3

1

3

0.9x1 +2.7x2 −3.9x3 = 2.41

7.6x1 +5.8x2 +4.7x3 =10.01

21.

2.51x1 +5.86x2 −0.5x3 = 3.96

22. 3.8x1 +4.1x2 +2.7x3 = 9.7

4.45x

−2.57x

2

+3.9x = −1.28

2.9x

+2.1x

2

+3.89x = 7.37

1

3

1

3

−3.3x1 +2.1x2 −4.3x3 = −0.21

5.4x1 −2.46x2 +3.9x3 =5.51

23.

4x1 −3.2x2 +5x3 = 6

24. 2.57x1 +6.28x2 −1.3x3 = 4.45

2x +1.23x

2

+3.5x = −1.2

2.71x −0.76x

2

+1.59x = −3.57

1

3

1

3

1. t2 −sin (t )= 45

2. −x5 = 2x +5

3. 2x −ln x =5

4. x3 −2x2 −4x +7= 0

5. x2 −cos2 πx = 0

6. 3x3 = x4

+3x2 −12

7. ex −6x −3+ tgx = 0, x [–π,π]

8. 2x2 = x4 −8x3 +16x −3

9.

−1/ x = 0

10. x3 −3x2 =10

x +1

11. 3x −cosx −1= 0

12. x3 −2x2 −4x +7= 0

13. 2ex =5x +2

14. x3 −6x2 = −20

15. x4 −5x3 −4x2 −3x +12= 0

16. x2 cos2x = −1

17. 2x2 = x4 −8x3 +16x −3

18. 5 = x2 −2x

19. ex+1 + x +

1

= 0

20. (x +1)5 +3x +

26 = 0

5

5

21.

x3

1

−

x

x

3

−

− x +

2

= 0

22. e

2 −

−

= 0.

8

2

2

x

x

11

2 −

−2x

+ 1 = 0

23.

−

24. ln

−

−

−

= 0

2

2

2

2

x

2

6. СИСТЕМЫ НЕЛИНЕЙНЫХ УРАВНЕНИЙ

Найти решение системы методом Ньютона с точностью ε =10−2

1.

sin(x +1)− y =1.2

2. sin x +2 y = 2

3.

sin(x −1)=1.3− y

2x +cosy = 2

cos(y −1)+ x = 0.7

x −sin(y +1)= 0.8

4. cos(y −1)+ x = 0.8

5. cos(x −1)+ y = 0.5

6.

cosx + y =1.5

y −cosx = 2

x +cosy = 3

2x −sin(y −0.5)=1

7. cos(x −1)+ y = 0.8

8. cos(y −1)+ x = 0.9

9. cos(y +0.5)+ x = 0.8

x −cosy = 2

y −cosx = 2

sinx −2y =1.6

10.

sin(x +0.5)− y =1.2

11. 2y −cos(x −1)= 0

12.

sin(x +0.6)− y = 0.5

x +cos(y −2)= 0

x +sin y = −0.4

cos(x −2)+ y = 0

13.

sin(y −1)+ x =1.3

14. sin(y +1)− x =1.2

15.

sinx +2y =1.6

y +sin(x +1)= 0.8

2y +cosx = 2

x +cos(y −1)=1

16. cos(x −1)+ y =1

17. 2x −cos(y +1)= 0

18.

cos(x +0.5)+ y =1

2x +sin y =1.6

y +sin x = −0.4

sin y −2x = 2

19.

cos(x +0.5)− y = 2

20. cos(y +0.5)− x = 2

21. cos(y −1)+ x = 0.5

sin y −2x =1

sinx −2y =1

y +cosx = 3

22.

cosx + y =1.2

23. sin(x +0.5)− y =1

24.

sin(x −1)+ y =1.5

2x −sin (y −0.5)= 2

x +cos(y −2)= 0

x −sin(y +1)=1

7. ЗАДАЧА КОШИ ДЛЯ ОБЫКНОВЕННОГО

ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ

Задача №1.

Получить численное решение дифференциального уравнения

y′= f (x,y),

удовлетворяющее заданному начальному условию y(x0 )= y0 на

Задача №2.

Получить численное решение дифференциального уравнения

y′= f (x,y),

удовлетворяющее заданному начальному условию y(x0 )= y0 на

Задача №3.

Получить численное решение дифференциального уравнения

y′= f (x,y),

удовлетворяющее заданному начальному условию y(x0 )= y0 на

1.

y′+

2 y2x

= 0,

y (0)=1,

x [0,5]

2.

y′= −yx + x,

y (0)= 2,

x [0,5]

x2 +1

3.

′

=

(y

2

−

1)x,

y (1)

=

2, x

[1,3]

4.

y

′

=

y

,

y 1

=1, x 1,2

x

2y y

( )

[

]