Challenge! Use Taylor series expansions to prove first-order Differential Equation
Suppose dy/dt = f(y) has an equilibrium point at y = y0 and
a) f'(y0) = 0, f''(y0) = 0, and f'''(y0) > 0: Is yo a source, a sink, or a node?
b) f'(y0) = 0, f''(y0) = 0, and f'''(y0) < 0: Is yo a source, a sink...