6200

№

f(x)

a

b

F(x)

вар.

1

x 2.3

0.2

2.2

(1/3.3)*x 3.3

2

1/x

1.6

3.8

ln|x|

3

2.3

x

0.9

2.63

2.3

x /ln2.3

4

e

0.8x

0.11

3.6

e

0.8x

/0.8

5

0.1 sin(x)+0.2 cos(x)

-π/4

π/4

-0.1 cos(x)+0.2 sin(x)

6

1/ cos2(x)

0

π/4

tg(x)

7

1/sin2(x)

0.1

π/4

-ctg(x)

8

1/(1+x2)

0.12

2.6

arctg(x)

9

1

0.18

2.5

ln|x+√ 2 + 1|

√ 2 + 1

10

1

1.1

2.8

ln|x+√ 2 − 1|

√ 2 − 1

11

1/(1-x2)

0.14

0.9

0.5*ln|1+ |

1−

12

x 1.2

0.1

3.21

(1/4.2)*x 4.2

13

2.8/x

1.7

4.0

2.8*ln|x|

14

4.1x

1

2.5

4.1x /ln4.1

15

e

2.1x

0.21

3.7

e

2.1x

/ 2.1

16

1.4 cos(x)-0.8 sin(x)

-π/5

π/5

1.4 sin(x)+0.8 cos(x)

17

2.6 / cos2(x)

0

π/3

2.6*tg(x)

18

0.92 / sin2(x)

0.2

π/3

-0.92*ctg(x)

19

2.1 /(1+x2)

0.11

2.5

2.1*arctg(x)

20

1.6

0.12

3.4

1.61*ln|x+√ 2 − 1|

√ 2 − 1

21

0.71

1.2

2.9

0.7*ln|x+√ 2 − 1|

√ 2 − 1

22

x 0.96

0.5

4.5

(1/1.96)*x 1.96

23

1.56 /x

1.75

4.2

1.56*ln|x|

24

1.21x

1.21

3.14

1.21x / ln2.3

25

e

0.98x

0.3

3.1

e

0.98x

/ 0.98

26

0.51 sin(x)-2.1 cos(x)

-π/6

π/4

-0.51 cos(x-2.1 sin(x)

27

0.32 / cos2(x)

0

π/3

0.32*tg(x)

28

1.19/ sin2(x)

0.3

π/4

-1.19*ctg(x)

29

1.18 / (1+x2)

0.13

2.7

1.18*arctg(x)

30

1.09

0.14

3.6

1.09*ln|x+√ 2 + 1|

√ 2 + 1

№

Дифференциальное

Началь

Интервал

Точное решение

ные

интегрир

дифференциального

вар

уравнение

условия

ования

уравнения

1

x2*y’ – x + 1=0

y(1)=1

[1;2]

y=ln(x) + 1/x

2

y’=(1+y2)*x

y(0)=0

[0;1]

y=tg(x2/2)

3

y’=x*ex-y

y(2)=2

[2;3]

y=x+ln(x-1)

4

y(1)=1

[1;2]

y=x*(ln√

+ 1)2

x*y’ – y –√ =0

5

y’=(y/x)+sin(y/x)

y(1)=π/2

[1;2]

y=2*x*arctg(x)

6

x*y’=x+2x

y(1)=0

[1;2]

y=(x-1)

7

y’=(y/x)+cos(y/x)

y(1)=0

[1;2]

y=2x*(arctg(x)- π/4)

8

y’+y/(x2)= e1/x

y(1)=0

[1;2]

y=(x-1)* e1/x

9

y’*cos(x)+y*sin(x)=1

y(0)=1

[0;1]

y=sin(x)+cos(x)

10

y’+(y/x)=2ln(x)+1

y(1)=1

[1;2]

y=x*ln(x)+(1/x)

11

ey*(1+x2)*y’–2x*(1+ ey)=0

y(0)=0

[0;1]

y=ln(2x2 + 1)

12

x*y’-y=x*tg(y/x)

y(1)= π/6

[1;2]

y=x*arcsin(x/2)

13

2xy+2y2=(x2+xy)*y’

y(1)=2

[1;2]

Y=2*x2

14

x*y’–3√2

-y=0

y(1)=1

[1;2]

y=x*(ln(x)/3 + 1)3

15

(x+1)*y’–3y=ex*(x+1)4

y(0)=1

[0;1]

y=ex*(x+1)3

16

(1+x2)*y’–2xy=(1+x2)2

y(0)=0

[0;1]

y=x*(1+x2)

17

y’+2y/(1-x3)=(1-x)/(1+x)3

y(0)=0

[0;1]

y=x*(1-x)/(1+x)2

18

xy’=xe-y/x+y

y(1)=0

[1;2]

y=x*ln(1+ln(x))

19

y’+y*cos(x)=0.5*sin(2x)

y(0)=0

[0;1]

y=e-sin(x)+sin(x)-1

20

y’–y*tg(x)=1/cos(x)

y(0)=1

[0;1]

y=(x+1)/cos(x)

21

y’–x*y=x2*ex2/2

y(0)=1

[0;1]

y=(x3*/3)*ex2/2

22

y’+y=1/ex

y(0)=0

[0;1]

y=x*e-x

23

y’+(3/x)*y=2/x3

y(1)=0

[1;2]

y=2(x-1)/x3

24

y’-2y=3x+1

y(0)=1/4

[0;1]

y=0.5*(e2x-3x-1/2)

25

y’=y*tg(x)+cos(x)

y(0)=0

[0;1]

y=(2x+sin(2x))/4cos(x)

26

y’–[sin(2x)/(cos2(x)+4)]*y=1

y(0)=0

[0;1]

y=(4.5x+.25sin(2x))/(4+cos2(x))

27

y’=[x/(1+x2)]*y

y(0)=8

[0;1]

y=8*√1 + 2

28

y’+[2xy/(x2-1)]=1/(x4-1)

y(0)=1

[0;1]

y=(arctg(x)-1)/(x2-1)

29

y’=(y/x)-tg(y/x)

y(1)= π/6

[1;2]

y=x*arcsin(1/(2x))

30

(y-x)*y*dy+x2*dx=0

y(1)=1

[1;2]

y=x/(1+ln(x))

31