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For each of the differential equations below, find the critical points, draw a phase diagram, and ...
For each of the differential equations below, find the critical points, draw a phase diagram, and for each critical point determine whether it corresponds to a stable or unstable solutions. (a) x?=x2?3x (b) x?=x(x+2)2 (c) x?=x2(9?x2).
Solution:- a) Consider Critical points x=0 and x=3 When flow up then and flow down then For linear stability at At x=0, At x=-3, So, x=0 is stable and x=-3 is unstable