ONE answer for EACH question Consider the autonomous equation y \' = y 3 ( y - 1

Question

ONE answer for EACH question

Consider the autonomous equation y ' = y 3 ( y - 1 ) 2 ( y + 2 ) .

The point y = 1 is . . .
stable.
semistable.
not stable.
The point y = 0 is . . .
stable.
semistable.
not stable.
The point y = - 2 is . . .
stable.
semistable.
not stable.
Which of the following integrating factors makes the equation - x sin y d x + ( 2 + x ) cos y d y = 0 exact?
µ = 1
µ = x
µ = e x
µ = ( x + 2 ) / e x
µ = sin x
Assume that your car has a braking system capable of decelerating the automobile at a rate of 10 meters per second per second ( m s 2 ) . If the brakes are applied when the car has reached a velocity of 30 m s , how far will your car travel before coming to a complete stop?
0 meters
3 meters
10 meters
15 meters
30 meters
35 meters
45 meters
90 meters

Explanation / Answer

1) Semistable 2) not stable 3) stable 4) µ = ( x + 2 ) / e x 5 ) 30 m

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