5. (1

+e

x

)y

′

=

ex

y

(0)=1,

x [0,2]

6.

′

+ x

2

,

y (1)=1,

x [1,4]

y ,

y x = y

7.

y′= (y +1)2 lnx,

y (1)=1,

x [1,2]

8.

y′= y −1,

y (1)= 2,

x [1,2]

9.

y

′

=

y

(x

−1)

,

y 1 = e, x

1,5

10.

y

′

+

y

=

x

2

,

y (1)

=

1,

x

[1,3]

x2

(

)

[ ]

x

11.

y′=

1+ xy

,

y

(1)= 0,

x [1,3]

12.

y′= x

+

2 y

,

y (1)=1,

x [1,2]

x2

x

13.

y′= yx,

y (1)=1,

x [1,2]

14.

y

′

=

y2 + yx

,

y (1)=1,

x [1,2.5]

x2

15.

y′=

1− y +lnx

,

y (1)= 0,

x [1,6]

16.

y′

=

y + x

,

y

(1)= 0,

x [1,3]

x

x

17. (x2 −1)у′= y2 ,

y (2)=1,

x [2,3]

18.

xу′+ y = y2 ,

y (1)=5,

x [1,3]

19.

xу′− y = y

3

,

y

(

0

)

= 2,

x

0,1

20.

(

y

2

+1 у

′

= x

2

,

y (0)=1,

x [0,2]

[

]

)

21.

y′− y = ex , y(0)=1, x [0,1]

22.

xy′−2 y = 2x4,

y(1)= 0,

x [1,3]

23.

y′+

y

= x2,

y(1)=1,

x [1,4]

24.

y′−

y

= −

12

, y(1)= 4,

x [1,2]

x3

2x

x

y′

y′′+

+2y = x;

x

1.

′

y(0.7)= 0.5,

2y(1)

+3y (1)=1.2.

2.

y′′− xy′+2y = x +1;

′

2,

y(1.2)=1.

y(0.9)−0.5y

(0.9)=

3.

y′′+ xy′+ y = x +1;

′

y

′

y(0.5)+2y (0.5)=1,

(0.8)=1.2.

13

= x

2

;

4. y′′+2y′− xy

y′(0.6)= 0.7,

y(0.9)−0.5y′(0.9)=1.

y

5.

y′′+2y′−

= 3;

x

′

y(0.2)

= 2,

0.5y(0.5)

− y (0.5)=1.

2 y

= x +0.4;

6.

y′′− y′+

x

′

′

y(1.1)

−0.5y

2,

4.

(1.1)=

y (1.4)=

y

7.

y′′−3y′

+

=1;

x

′

y(0.4)

= 2,

y(0.7)+2y (0.7)= 0.7.

y

8.

y′′+3y′−

y = x +1;

x

′

′

y (1.2)=1,

2y(1.5)− y (1.5)= 0.5.

y′

3y = 2x2;

9.

y′′

−

+

2

′

y(1)

+2y

y(1.3)=1.

(1)= 0.6,

10.

y′′+1.5y′− xy = 0.5;

′

1,

y(1.6)= 3.

2y(1.3)− y

(1.3)=

y′′+2xy′− y = 0.4;

11.

′

1,

′

2.

2y(0.3)+ y

(0.3)=

y (0.6)=

12.

y′′−0.5xy′+ y = 2;

=1.2,

′

1.4.

y(0.4)

y(0.7)+2y (0.7)=

2 y′

−3y = 2;

y′′+

x

13.

′

′

y (0.8)=1.5,

2y(1.1)+ y (1.1)= 3.

2

y′+

y = x;

14.

y′′+2x

′

y(0.8)= 3.

2y(0.5)− y (0.5)=1,

15.

y′′−3xy′+2y =1.5;

′

0.5y(1)

′

y (0.7)=1.3,

+ y (1)= 2.

16.

y′′+2xy′−2y = 0.6;

′

′

y (2)=1,

0.4y(2.3)− y (2.3)=1.

y′

y′′+

−

0.4y =

2x;

x

17.

′

′

y(0.6)

−0.3y

(0.6)= 0.6,

y (0.9)=1.7.

y′

18.

y′′−

+0.8y = x;

2x

′

′

y(1.7)+1.2y

(1.7)= 2,

y (2)=1.

y′

19.

y′′−

+ xy

= 2;

3

′

y(0.8)=1.6,

3y(1.1)−0.5y (1.1)=1.

y

1

20.

y′′

+2y′−

=

;

x

x

′

y(1.2)= 0.8.

0.5y(0.9)+ y (0.9)=1,

21.

y′′−0.5xy′+ y = 2;

′

y(0.4)=1.2,

y(0.7)+2y (0.7)=1.4.

22.

2

;

y′′+2y′− xy = x

y′(0.6)= 0.7,

y(0.9)−0.5y′(0.9)=1.

y′

y′′+

−

0.4y =

2x;

x

23.

′

′

y(0.6)

−0.3y

(0.6)= 0.6,

y (0.9)=1.7.

y′′− xy′+2y = x +1;

24.

′

y(1.2)=1.

y(0.9)−0.5y (0.9)= 2,

4.

СИСТЕМА ЛИНЕЙНЫХ АЛГЕБРАИЧЕСКИХ УРАВНЕНИЙ

9

5.

НЕЛИНЕЙНЫЕ УРАВНЕНИЯ…………………………………..

11

6.

СИСТЕМЫ НЕЛИНЕЙНЫХ УРАВНЕНИЙ……………………

11

7.

ЗАДАЧА КОШИ ДЛЯ ОБЫКНОВЕННОГО

ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ…………………………

12

8.

КРАЕВАЯ ЗАДАЧА ДЛЯ ОБЫКОВЕННОГО

ДИФФЕРЕНЦИАЛЬНОГО УРАВНЕНИЯ…………………………

13

БИБЛИОГРАФИЧЕСКИЙ СПИСОК………………………………

16