 
Summary: Worksheet 6: Seperable DE's
Fall 2011, Kennedy
NAME:
Website: http://math.ucsb.edu/kgracekennedy/Fall2011 3C.html
Course Website: Access through GauchoSpace.
1 Autonomous vs. Nonautonomous DE's and
Direction Fields, 3C
1. Consider the differential equation
y = 4 + y2
(a) Is this DE autonomous or nonautonomous? 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 longterm 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
know yet
how to solve
nonseperable
