Homework Help: Critical Points and Graphs of Differential Equations

Consider the equation dy/dt = alpha - y^2

a) Find all of the critical points. How does it change as alpha < 0, alpha = 0 or alpha > 0?

b) In each case of different alphas, consider the graph of f(y) vs y and determine whether each critical point is asympototically stable, semistable, or unstable.

c) For alpha > 0, find the solution.

d) Plot a bifurcation diagram - this is a plot of the location of the critical points as a function of alpha (plot a graph alpha as x axis and y axis showing the location of the critical point)