Вариант 6
1.y' x 1y 2 0.
2.xy' y y 2 .
3.xy' cos y sin y 0.
4.xy' y arctg xy x.
5.y'' sin 4 x sin 2x.
6.y'' y' tgx sin2x.
7.y'' y ctgx.
8. |
y''' 2 y'' y' x2 e x . |
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9. |
yy'' y'2 y'3 , y 0 y' 0 1. |
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y''' 2 y'' 0, y 0 0, |
y' 0 1, |
y'' 0 4. |
11.x' y tg2 t 1,y ' x tgt.
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Вариант 7 |
1. |
e x2 y' 2xyex2 |
x sin x. |
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dy 0. |
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3.xy 
x dy ydx 0.
4.y'' x cos3 x.
5.xy'' y' x2 e x .
6.y'' y' 2 1 0.
7.y'' 3y' 2 y e3x x2 x .
8.y'' y' cos1 x .
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9. xy' |
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y 1 |
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y 1 |
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10. y''' |
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y 0 2, |
y' 0 0, |
y'' 0 1. |
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dx 2x y,
11.dt
dy 2 y x 5et sint.
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Вариант 8
1.sin2 y ytgx dx 2xcos2 y lncosx 2 y dy 0.
2.xex y' yex 1.
3.1 y 2 dx xydy 0.
4.xy x dy ydx 0.
5. y'' |
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cos 2x. |
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6.1 x2 y'' 2xy' x3 .
7.y'' y tg2 x.
8.y'' 3y' 10 y sin x 3cos x.
9. yy'' y' 2 y' 3 0, y 0 1, y' 0 2.
10. y''' 2 y'' 10 y' 0, y 0 2, y' 0 1, y'' 0 1.
11.x' 2x y,
y' y 2x 18t.
Вариант 9
1. y' xy 1 ln y ln x .
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2.y' sin x y ln y.
3.2 y ln y y x y' y.
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5. |
y'' |
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6. |
y |
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y'' e x x. |
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7. |
y''' 2 y''' |
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8.y'' 2 y' 2 y e x cos1 x .
9.2 yy'' y' 2 , y 1 4, y' 1 1.
10. y'' 4 y' 4 y 0, y 0 3, y' 0 1.
11.x' x 2 y,y' x 5sint
Вариант 10
1.xy' cos xy y cos xy x.
2.2x 1 dy y 2 dx 0.
3. |
y' |
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x cos y sin 2 y |
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4. |
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3x sin y 1 dx |
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5.y'' cossin 42xx .
6.xy'' y' ln y' ln x .
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7.y''' y' 1 cos x.
8.y'' 3y' 2 y 1 e2ex2 x .
9. y'' e y , y / x 0, |
y' / x 0 2. |
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10. |
4 y'' |
4 y' y 0, |
y 0 2, y' 0 0. |
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y cost; |
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11. |
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x sint. |
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Вариант 11
1. y' ytgx cos1 x .
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xy |
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x ln x dy 0. |
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2 2xy |
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3.1 e x yy' ex .
4.x2 y 2 2xyy' 0.
5.y'' x cos 2x.
6.x2 y'' x2 y' 1.
7. y'' y' cos2 x e x x2 .
8. |
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2 y |
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e x |
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4 x2 |
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9. |
y 3 y'' 1, |
y 1 1, |
y' 1 1. |
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y'' 6 y' |
9 y 0, |
y 0 0, |
y' 0 2. |
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11.x' 2x y,y' x 2et .
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