Материал: 864
dx
11.dtdy 2x 8y;
x 4y.
dt
Вариант4
1. y |
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3.y
x2 1y x.
4.x2 y (2x y)y 0.
5.xy 2y x4. |
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6.x |
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0, y (1) 1. |
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7.(1 x |
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8.y 25y 0. |
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9.y 16y 3x 1. |
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10.y(4) |
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9y 0. |
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dx |
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11. dt |
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dy |
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7x 3y. |
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dt
Вариант 5
1.y 
3x 1 y 1.
2.xy y 1.
3.(x2 1)dy xydx;y |x 0 2.
4.xy y 
x2 y2 .
5.x2 y 2xy 3.
6.y 24x 4; y(1) 1; y (1) 1;y (1) 1.
7.2xy y .
8.y 16y 0.
9.y 6y x2 1;y(0) 1; y (0) 2 . 8 27
10.4y y 0.
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dx
11.dydt 3x y;
8x y.
dt
Вариант 6
1.x2 
4y 1 y .
2.x(y2 1)y y.
3.x(y 2)dy dx.
4.y x y.
xy
5.y x y.
xy
x
6.y e 2 ;y(0) 0;y (0) 0;y (0) 0,5.
7.y xln x y .
8.y 2y 2y 0.
9.y |
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3y |
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3x |
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2; y (0) |
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10.y 9y 0.
dx
11.dtdy 2x 3y;
x 4y.
dt
Вариант 7
1.x(y 1)dx (x2 1)ydy 0.
2.xy y2 1 0;y(1) 0.
3.y
1 x2dy y2dx 0.
4.xyy x2 y.2
5.xy y ex.
6.y 5x4 2x3 x2; y(1) 0,25;y (1) 0.
7.y tgy 2(y )2.
8.3y 2y 0.
82
9.y 2y 3x;y( 1) 0;y ( 1) e 2.
10.y(4) 16y 0.
dx
11.dtdy 4x y;
8x y.
dt
Вариант 8
1.2xy y.
2.y sin x yln y.
3.(1 y2 )dx xydy 0.
xy
4.y y x;y |x 1 1.
5.y ycosx sin xcosx;y |x 0 0.
6.y cosx; y(0) 0; y (0) 1; y (0) 0.
7.x2 y (y )2.
8.y 5y 0.
9.y 3y x 2; y(0) 0; y (0) 1.
10.y(4) 5y 0.
dx
11.dydt 4x 6y;
4x 2y.
dt
Вариант 9
1.y |
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y2 |
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x2 |
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2.xy y2 3. 2y
3.dy=ytgxdx; y( ) 2.
4.x2 y2 2xyy 0.
5.x2 dy 2xy 3;y( 1) 1. dx
83
x
6.y e 3 ;y(0) 3; y (0) 9;y (0) 27.
7.(1 x)y y 0.
8.y 7y 0.
9.y 4y cos x; y(0) 1; y (0) 0.
10.y 2y y 0.
dx
11.dydt x 3y;
3x y.
dt
Вариант 10
1.y 1 y2.
2.2xsin ydx (x2 1)cos ydy 0;y(1) .
4
3.xyy 1 x2.
4.xy 2
xy y.
5.y x2 y x2;y |x 2 1.
6.y 8sin2x 1; y(0) 0; y (0) 2; y (0) 0.
7.y 5y.
8.y 4y 4y 0.
9.y 6y 9y e3x;y(0) 1;y (0) 0.
10.y(4) 16y 0.
dx
11.dydt 5x 4y;
2x 3y.
dt
Вариант 11
1.y 
1 x2 y.
2. (1 ex)yy ex; |
y(1) 1. |
3.x
4 y2 dx y
1 x2 dy 0.
y
4.xy y xex .
84
5.y 3y e x.
6.y 16cos2x; y(0) 0; y (0) 1; y (0) 0.
7.(2y y )y (y )2.
8.y 3y 2y 0.
9.y 9y 6e3x;y(0) 0;y (0) 0.
10.4y(4) 3y y 0.
dx
11.dydt x 2y;
4x 3y.
dt
Вариант 12
1.y y2 y.
2.y sin x ey.
3.(xy2 x)dx (y x2 y)dy 0.
4.(x y)dx xdy 0.
5.xy y x2.
6.y 81e 3x; y(0) 0;y (0) 0;y (0) 0.
7.xy y ln(y / x).
8.y 4y 3y 0.
9.y y 4ex;y(0) 4; y (0) 3.
10.y(4) 16y 0.
dx
11.dydt x 5y;
7x 3y.
dt
Вариант 13
1.y cosx (y 1)sin x.
2.(x2 1)y 2x(4 y);y(0) 1.
3.y
x 1dy (y2 1)dx 0.
4.(2x y)dx (x y)dy 0.
5.xy y 3 0.
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