MathCastle
Differential EquationsChallengeExistence, Uniqueness & Bifurcations

Existence, Uniqueness & Bifurcations · Challenge problem

The equation y ′=ry−y3y\,\prime = ry - y^3 undergoes a pitchfork bifurcation at r=0r = 0. For r=9r = 9, how many equilibria are there, and what is the largest one? Give the largest equilibrium.