Consider the differential equation dy dt

= (1 + y)(1 − y).

a. What are the steady states?

b. Using a computer package such as Wolfram Alpha or Matlab, can you find an exact solution (i.e., can you find the solution in the form y(t))?

c. Using any method you like, determine what happens to the solutions with the initial condition i. y(0) = 0.
ii. y(0) = 0.5.
iii. y(0) = 1.5.
iv. y(0) = −0.5.
v. y(0) = −1.
vi. y(0) = −225.6 Consider the differential equation du dm = f (u).
Show that if there are no nodes the steady states must be alternating sinks and sources.