Differential eqns
posted by Erica on .
a) Sketch the phase line for the differential equation
dy/dt=1/((y2)(y+1))
and discuss the behavior of the solution with initial condition y(0)=1/2
b) Apply analytic techniques to the initialvalue problem
dy/dt=1/((y2)(y+1))), y(0)=1/2
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
http://www.sosmath.com/diffeq/first/phaseline/phaseline.html
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.