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Differential Equationshard
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An autonomous equation dydt=f(y)\frac{dy}{dt} = f(y)dtdy​=f(y) has equilibrium solutions at y=−1,0,1y = -1, 0, 1y=−1,0,1. If f′(−1)<0f'( -1) < 0f′(−1)<0, f′(0)>0f'(0) > 0f′(0)>0, and f′(1)<0f'(1) < 0f′(1)<0, what can be said about the stability of y=0y=0y=0?