Real stabilization graphs

Analyze the following equations graphically. In each case, sketch the vector field on the real line, find all the fixed points, classify their stability, and sketch the graph of x(z) for different initial conditions. Then try for a few minutes to obtain the analytical solution for x(z) if you get stuck, don t try for too long since in several cases it s impossible to solve the equation in closed form ... 

Investigate the stability of the equilibrium points of the system X - x- a)(x - o) for all real values of the parameter a. (Hints It might help to graph the right-hand side. An alternative is to rewrite the equation as x = -V x) for a suitable potential energy function V and then use your intuition about particles moving in potentials.)... 

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