Help with parts (b)-(d)?

Also the ODE is ?x?=(x+1)(x?1)(x?2)2(x?3)?

Consider the scalar ODE w'(w + 1)(:z: 1)(:.c 2)2({B 3). [One can solve this by sophomore differential equations methods, but doing so it not necessary, or even particularly useful, in answering this question. Note that this is an ODE to which our elementary arguments show that there is exactly one maximal solution satisfying any initial condition $020) = 35'0- (a) What are the equilibrium solutions? (b) Consider an initial condition {5(0) = mg. For which :30 will the graph of the solution have a horizontal asymptote as t > 00? (c) Consider an initial condition {3(0) = $0. For which are will the graph of the solution have a horizontal asymptote as t > 00? (d) Consider an initial condition :r:(0) = $0. For which we might the graph of the solution have a vertical asymptote