Differential Equationshard
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An autonomous differential equation is defined by dydt=g(y)\frac{dy}{dt} = g(y). If g(y)g(y) has roots at y1=1y_1 = -1, y2=1y_2 = 1, and y3=2y_3 = 2, and the derivative g(y)g'(y) satisfies g(1)<0g'(-1) < 0, g(1)>0g'(1) > 0, and g(2)<0g'(2) < 0, which of the following statements correctly identifies the stability of these equilibrium points?