# 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)

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Simon Bridge
Homework Helper
To get the best out of these forums, you should show us your attempt at the problem so we can target assistance to the place you most need it.

For example - do you know how the critical points of y are related to dy/dx ?

hey mate post up what you've done and i'll show you the next steps

the diff plots can be daunting in the beginning but if you keep practicing them they become very easy to interpret

let us know