3. (a) Consider the following first-order vector fields:

i) x = cos(2x+1),

ii) x= x(2-x²)(x+3).

For each of them, plot the velocity function v(x), identify the equilibrium points, and find

the stability of the equilibrium points using linearization about the equilibria. You should

also relate the reasoning to the geometry of velocity functions around the equilibrium

points.

(b) Consider the second-order equation X=(x-2)(x² −2)=f(x,^). It depends on the

parameter A. Find the equilibrium points of the system and their stability. Consider the

cases for λ ≤ 0, 0 < λ < 1, λ = 1 and a > 1.