I please need help with this homework problem... It's due in 2 days. Than You much in advance. Here it is:
1) Consider the two differential equations:
dx/dt= (x-1)(x-2)(x-3)
and
dx/dt= (1-x)(2-x)(3-x)
For each equation, find the critical points and the equilibrium solutions, and construct the phase diagram and determine the stability of the critical points. Then, without attempting to solve the equation explicitly, make rough sketches of typical curves. You should see two funnels and a spout in one case, two spout and a funnel in two in the other.