Материал: 864
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;y(2) 0;y (2) 1. |
7.y (x2 1) 2xy ;y |x 0 1;y |x 0 3.
8.y 4y 0.
9.2y 5y 5x2 2x 1; y(0) 1;y (0) 17.
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10.y(4) 5y 0.
dx
11.dydt 5x 8y;
3x 3y.
dt
Вариант 14
1.(1 x)y 1;y(1) 2. y
2.
ex 1y ex.
3.xydx 
1 x2 dy 0.
y
4.xy y xex .
5.xy 3y x2.
6.y 1 1; y(1) 0;y (1) 2. x
7.y 2xy 0.
8.y 2y y 0.
9.y 4y e 2x;y(0) 0;y (0) 0.
10.y 6y 9y 0.
dx
11.dt x 5y;dy x 3y.
dt
Вариант 15
1.x3 y y 1.
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2.(1 x)y 2;y(1) 4. 2
y
3.xln xdy (5 y)dx 0.
4.xy y xtg y.
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6.y x 3e2 5x.
7.(1 sin x)y y cos x 0.
8.y 7y 0.
9.y y 2cos; y(0) 1; y (0) 0.
10.y 10y 25y 0.
dx
11.dydt x 3y;
x 5y.
dt
Вариант 16
1.(y 2)y sin2x; y(0) 1.
2.xy2dx dy.
3.y2 y 2x 1 0.
4.xdy ydx 
x2 y2 dx.
5.xy y x 1 0.
6.y |
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;y(0) 1; y |
(0) 2; y (0) 1. |
7.y 1 y x2. x
8.y 4y 0;y(0) 0; y (0) 0.
9.y 4y 6x2 1;y(0) 2; y (0) 3.
10.y(4) 3y 0.
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dx
11.dydt 3x y;
8x y.
dt
Вариант 17
1.y 1 sin2x; y(0) 1.
2.
1 x2 y x
1 y 0.
3.yy xey 0.
4.(x2 y2)y 2xy.
5.xy 2y (x 3)xy2; y(1) 4.
6.(1 x2)y xy .
7.y sin 2x.
8.9y 12y 4y 0; y(0) 0; y (0) 1.
9.2y y 3sin x.
10.y(4) 4y 0.
dx 2x 4y 4t 1;
11. dt |
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x(0) 5; y(0) 1. |
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Вариант 18
1.2x2 y 5y 1 0; y(0) 1.
2.(4x 1)y cos2 2y.
3. dy x2 ydx 0. x 2
4.yy 2y x.
5.y x y xy2.
6.y y ln y ; y(0) 0; y (0) 1.
7.2xy y ; y(9) 8; y (9) 3.
8.y xsin x; y(0) 0; y (0) 0.
9.y 6x 13y x.
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10.y(4) y 0.
dx
11.dydt x 4y;
2x 3y.
dt
Вариант 19
1.y ctgx y 2; y(0).
2.3y y 3
x 0.
3.(xy2 x)dx (x2 y y)dy 0.
4. xy y(1 ln y); y(1) 1 .
x
e
5.t2 ds 2ts 3; s( 1) 1. dt
6.y xln x y ; y(e) e 1; y (e) 1.
7.y 2
1 y ; y(0) 5; y (0) 1.
8.y sin2 x; y(0) 5; y (0) 1; y (0) 0.
9.y y x 1.
10.y(4) 8y 0.
dx
11.dtdy 2x 8y;
x 4y.
dt
Вариант 20
1.
1 ln ydy xydx 0.
2.y 2y 1 0.
3.
x2 1dy yxdx 0.
4.y 
x2 y2 xy 0.
5.y y sin x; y( ) 1.
xx 2
6.y (x2 1) 2xy ; y(0) 1; y (0) 3.
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9.y y 2cos x.
10.y(4) 16y 0.
dx
11.dydt 5x 4y;
2x 3y.
dt
Вариант 21
1.y ytg2x 0.
2.xy _3y 2 0.
3.
1 yy x 1 0.
y
4. y ex y. x
5. (1 x2)y xy xy2; y(0) 0,5.
6. y cosx y sin x 0; y(0) 1; y (0) 2. 4
7.3yy (y )2 0.
8.y (x 5)2 1; y( 1) 1 ; y ( 1) 1.
12 4
9.y 6y 9y 10sin x.
10.y 2y 0.
dx
11.dtdy 7x 2y;
3x 2y.
dt
Вариант 22
1.(1 x2)y xy 0.
2.xy y 3 0.
3.y tgy 2x2.
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