Summary: Worksheet 6: Seperable DE's
Fall 2011, Kennedy
Website: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
1 Autonomous vs. Non-autonomous DE's and
Direction Fields, 3C
1. Consider the differential equation
y = 4 + y2
(a) Is this DE autonomous or non-autonomous? Is it separable?
(b) Draw the direction field for this DE. Mark all constant solutions and
their stability classification
(c) What can you tell me about the long-term behavior of this model?
i.e. As time goes on, what can we say about y? Include information
about basins of attraction if applicable.
(d) If possible, find the general solution for this DE. Note that
you do not
how to solve