Chapter 16, Problem 39PE

(a)

To determine

To evaluate: The equilibrium values for the differential function $\frac{dy}{dx}=y^2-1$ and also to determine the values which are stable and unstable.

(b)

To determine

To sketch: The phase line and identify the signs of $y^{\prime }\text{and }{y}^{″}$ for the differential equation $\frac{dy}{dx}=y^2-1$.

(c)

To determine

To sketch: The representative selection of solution curves.