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We know that a given differential equation is in the form \( y^{\prime}=f(y) \), where \( f \) is ...
We know that a given differential equation is in the form \( y^{\prime}=f(y) \), where \( f \) is a continuous function of \( y \). Suppose that \( f(10)=0, f(9)=3 \), and \( f(11)=-3 \) This means that \( y=10 \) is a stable equilibrium. This does not tell us for certain that \( y=10 \) is an equilibrium. \( y=10 \) is an equilibrium, but it might not be stable.