Posted by **Erica** on Sunday, February 3, 2013 at 2:51pm.

a) Sketch the phase line for the differential equation

dy/dt=1/((y-2)(y+1))

and discuss the behavior of the solution with initial condition y(0)=1/2

b) Apply analytic techniques to the initial-value problem

dy/dt=1/((y-2)(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.

- Differential eqns -
**Steve**, Sunday, February 3, 2013 at 2:59pm
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).

- Differential eqns -
**Erica**, Sunday, February 3, 2013 at 4:22pm
I read the info, but it doesnt talk about functions with no equilibrium point.

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