posted by Erica .
a) Sketch the phase line for the differential equation
and discuss the behavior of the solution with initial condition y(0)=1/2
b) Apply analytic techniques to the initial-value problem
and compare your results with your discussion in part (a).
I couldn't get the equilibrium points for the equation so I did the phase line without them, and everything above 2 and below -1 was positive and between 2 and -1 is negative.
When y(0)=1/2, the solution is negative but what happens when it gets to 2 or -1 if they are not equilibrium points? And I don't really understand what they are asking for in part b.
The page at
has quite a lengthy and clear discussion of phase lines and equilibrium points.
Part (b) wants you to solve the equation analytically and compare the solution with your qualitative analysis in part (a).
I read the info, but it doesnt talk about functions with no equilibrium point.