Slope fields:Can y converge on two roots?

[craighenn]

For simple differential equations like y'=y(y-3) where there 2 roots, is it possible for y to approach y=root for both roots? Or must one diverge while the other converges? For multiple roots, can it only converge on one root, the others all diverging?

If it can converge on multiple roots, can you provide an equation example?

 

[Number Nine]

What do you mean "converge to both roots"? The fate of y will depend on the initial condition. Certainly, no initial condition can result in y converging to both 0 and 3, since limits are unique. In the case of your example, one fixed point is stable and the other is unstable.