# Math Help - differential equations

1. ## differential equations

sketch typical solutions for the following differential equations
indicate the set of points for which dy/dx = 0 by a dotted curve and determine the stability of any equilibria

can someone solve one example of this in full detail so i can attempt the rest

dy/dx = y(y-1)(y-2)

2. Solve y(y-1)(y-2)=0 to get the equilibria y=0,1,2.

To check stability say for y=0, note that
for solutions y with initial values near 0, we have dy/dt<0,
and so the solutions tend to the equilibrium when y>0 and diverge to infinity for y<0. Thus y=0 is unstable.