# Differential eqns

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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

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 - ,

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 - ,

I read the info, but it doesnt talk about functions with no equilibrium point.