diff_ur_zadaniya_tr_5354.ru

Вариант 17

1) (x 1)y0 + 2xy2 = 0:

2) xydy + (y + 1)dx = 0; yjx=1 = 0:

3) (x + 3y) = (y + 3x)y0:

4) y0

= y2=(xy x2):

5) y0 + xy = x4:

6) y0

= 3y + 3x; yjx=0 = 0:

7) y00 tg x = y0 + 1:

8) y00 + 2=y3 = 0:

8

dx

= x + 5y;

dt

>

>

>

>

>

14)

< dy

>

= 7x + 3y:

>

>

> dt

1) p

Вариант 18

dy = xydx:

2) y2xdx = (x 1)dy; yjx=2 = 1:

x2 + 1

3) y0 = (4x

y)=(y

x):

4) (x2 + y2)dy = xydx:

y

5) y0 = 2y 4x:

6) y0+

+2x3 1 = 0; yjx=1 = 0; 5:

x

7) y00 tg x = y0:

8) (y0)2 + 1 = y00=y0:

9) 4y00 + y = 0; yjx= = 1; y0jx= = 2:

10) y00

+ 4y0

+ 4y = e 2x:

11) y00 + 4y0

= 2 cos 2x:

12) y00

+ 6y0

+ 9y = 10 sin x:

13) y00 4y0

+ 5y = 2x2 e x:

8

dz

= 4z + 6y;

> dx

>

>

>

>

14)

< dy

>

= 4z + 2y:

>

>

Вариант 19

1) xydx + (x + 1)dy = 0:

2) y2 1 + 2x2yy0 = 0; yjx=1 = 2:

3) (x + y)dx = (x

y)dy:

4) xy0

= y + x

tg

(y=x):

y0

2y

5) y0 + y=x = 3 sin x:

6)

+

3x2 +2x= 0; yjx=1

= 2:

x

x

7) x3y00 + x2y0 = p

8) yy00 = yy0 + (y0)2:

x:

9) y00 9y = 0; yjx=0 = 2; y0jx=0 = 1:

10) y00

+ 9y = cos 3x:

11) y00

20y0 + 100y = sin 10x:

12) y00

+ y = e x:

13) y00

6y0 + 9y = x2 x + 3:

8

dx

= 2x + 3y;

>

dt

>

>

>

>

14)

< dy

>

= x + 4y:

>

>

> dt

Вариант 20

1) y0(2 x) = ctg y; yjx=0 = 0:

2) xdx + (y x2y)dy = 0:

3) (x 3y) = (y 3x)y0:

4) xdy + (x e y=x + y)dx = 0:

y0

3y

y

5)

+

+ 2x3 1 = 0:

6) y0 +

+ sin 2x = 0; yjx= = 1:

x

x2

x

7) (x + 1)y00 + y0 = x + 1:

8) 2yy00 = 1 + (y0)2:

9) y00 81y0 = 0; yjx=0 = 0; y0jx=0 = 1:

10) y00

6y0 + 13y = 1 + 26x:

11) y00

+ 4y = x sin 2x:

12) y00

+ 6y0 + 9y = 5 sin x:

13) y00

+ y0 = e x

8

dx

= 4x + y;

>

dt

>

>

>

>

14)

< dy

>

= 8x + 2y:

>

>

dt

>

>

Вариант 21

1) y0(x x2) = y; yjx= 1 = 1:

2) 2x2yy0 + y2 = 2:

3) y0 = (x + 4y)=(4x + y):

4) xy0 y ln (y=x) = y:

7) (1 + sin x)y00 = y0 cos x:

8) y00 + 2y(y0)3 = 0:

9) 0; 25y00 4y0 + 16y = 0; yjx=0 = 2; y0jx=0 = 1:

10) y00

+ 4y = cos 2x:

11) y00 y=4 = 9x 2:

12) y00

+ 3y0 = 9 e 3x:

13) y00 + 4y0 2y = sin 2x:

8

dx

= y

x;

>

dt

>

>

14) >

>

>

< dy

y:

>

= x

>

> dt

2

2

x:

p

1) y0(2 + x

) = 2y

2) y0 = (y + 2)= x; yjx=1 = 0:

3) py(py + p

) = xy0:

4) (x

3y)dx

(y

3x)dy = 0:

x

5) y0 + y=x = 3 cos x:

6) y0 y = 1 3x;

yjx=0 = 2:

7) xy00

p

8) 2yy00

2

:

+ y0 = 1= x:

= (y0)

9) 0; 5y00 + 0; 5y = cos x;

yjx=0 = 1;

y0jx=0 = 0

10) y00

+ 6y0 + 8y = 4 e 2x:

11) y00

+ 8y0 + 9y = 26x 1:

12) y00

+ 2y = 3 sin x:

13) y00

12y0 28y = e x(x 2):

8

dx

= 3y

8x;

>

dt

>

>

>

>

14)

< dy

>

= 7y

x:

>

>

> dt

Вариант 23

1) yy0=(y + 2) = 1 x:

2) y0(xy2 + 2xy) = 1; yjx=1 = 2:

3) (y + 2x) = y0(x + y):

4) xdy (r

+ y)dx = 0:

x2 y2

5) y0

3y + 2

x = 0:

6) y0 =

y

+

p

1

; y x=1 = 1:

x

1 + x

j

7) 2y0 xy00 = 2=x2:

8) y00y3 + 1 = 0:

12) y00

+ 6y0 + 13y = e 3x: 13) y00 24y0 + 144y = 3 sin 5x:

8

dy

= 5y

z;

> dx

>

>

>

>

dz

14)

<

>

= y + 5z:

>

>

Вариант 24

1) (x2 + 2)dy = 3xy3dx:

2) y0(y + 1)(x + 2) = x; yjx=0 = 1:

3) y0

= (x + 2y)=(2x

y):

4) y2 + x(x + y)y0 = 0:

p

5) y0

6) xy0+y 2x+

1

2

= 0; yjx= 1

+ y=x = 3=

x

+ 3:

= 0:

x

7) x4y00 + x3y0 = 4:

8) y00(2y + 3)

2(y0)2 = 0:

12) y00

4y0 + 4y = e 2x:

13) 2y00 + 4y0 + 2y = 5x2 32x + 5:

8

dx

= 4x + y;

dt

>

>

>

>

>

14)

< dy

>

= 8x + 2y:

>

>

dt

>

>

Вариант 25

1) ydy + (x y2x)dx = 0:

2) (x 1)y0

= y2 + 3y; yjx=0 = 1:

3) x2y0 = x2 + xy + y2:

4) (x + 3y)dx + (3x

y)dy = 0:

2x + 1

5) xy0

+ y +

= 0:

6) y0 + 3y + e 2x = 0; yjx=0 = 1:

x2

7) y00 + 2xy0=(x2 + 1) = 2x:

8) y0 = q

:

2yy00

9) y00 8y0 + 16y = 0; yjx=0 = 0; y0jx=0 = 1:

10) y00

+ 3y0 = 9x:

11) y00 + 4y0

+ 5y = 5x2 32x + 5:

12) y00

+ y = x cos x:

13) y00 + 4y0

+ 4y = e 2x:

8

dx

= 2x + 3y;

>

dt

>

>

>

>

14)

< dy

>

= x + 4y:

>

>

dt

>

>

>

>

:

Вариант 26

1) r

2) 2x3yy0 = 2 y; yjx=0;5 = p

:

y2 + 1

dx = xydy:

2

3) y0 = (x + 3y)=(3x + y): 4) (x2 2xy)dy + y2dx = 0:

5) y0 2y + 3x 1 = 0:

6) y0

y

p

2

+

x

+ 1 = 0; yjx=1

= 1:

x

7)

xy00

=

1

:

8) y00

= (y0)2 ctg y:

y0

ln x

9) y00 + 3y0 + 2y = 0; yjx=0 = 1; y0jx=0 = 2:

10) y00 2y0

+ y = 3 e x:

11) y00 + 3y0

= x 2x2:

12) y00 3y = (x 1) e x:

13) y00 + 5y0

+ 6y = 2 cos 3x:

8

dx

=

y;

> dt

>

>

>

>

14)

< dy

>

= x

2y:

>

>

> dt

Вариант 27

1) xydy + (1 y)dx = 0:

2) y0(x2 +1)+2xy2 = 0; yjx= 1 = 1:

3) (2y + x)dx = (2x

3y)dy:

4) (x2 + y2)y0 = xy:

5) y0 = ( e x y)=x:

6) y0 = y + 2x 3; yjx=0 = 3:

7) x2y00 5 = y0:

8) 3y = (y0)2y00:

9) y00 5y0 + 30y = 0; yjx=0 = 1; y0jx=0 = 0:

10) 4y00 4y0 + y = 25 sin 2x:

11) y00

+ 2y0 + 3y = 2x e x:

12) y00 + 5y0 = e 5x:

13) y00

+ y = cos x 2 sin x:

8

dx

= 4x

6y;

> dt

>

>

>

>

14)

< dy

>

= 4x + 2y:

>

>

> dt

Вариант 28

1) (1+2y)xdx= (1+2x2)dy:

2) xydy + (y + 1)dx = 0; yjx=1 = 0:

3) (5x + y)y0 = x + 5y:

4) y0 =

y

+

x

:

x

y

5) y0 y=x = 2 sin x:

6) y0 + 2y e x = 0; yjx=0 = e :

7) xy00

y0 = 1=x:

8) (y0)2 3yy00 = 0:

9) 4y00 + y = 0; yjx= = 1; y0jx= = 2:

10) y00

+ 64y0 = 0; 5:

11) y00

+ 9y = cos 3x:

12) y00

+ 6y0 + 9y = 3x e x:

13) y00

6y0

+ 13y = x2 + 1:

8

dx

= 4x + y;

>

dt

>

>

>

>

14)

< dy

>

= 8x + 2y:

>

>

> dt