Suppose dy/dt = f (y) has an equilibrium point at y = y0 and
(a) f ʹ (y0) = 0, f ʺ (y0) = 0, and f ʹʺ (y0) > 0: Is y0 a source, a sink, or a node?
(b) f ʹ (y0) = 0, f ʺ (y0) = 0, and f ʹʺ (y0) < 0: Is y0 a source, a sink, or a node?
(c) f ʹ (y0) = 0 and fʺ (y0) > 0: Is y0 a source, a sink, or a node?
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