Chapter 1.5, Problem 17E

(a)

To determine

To calculate: To prove that the differential equation $\frac{dy}{dt}=f(y)$ has the function f(y₀)=0.

(b)

To determine

To calculate: To sketch the slope field along the line y=y_o in the ty-plane.

(c)

To determine

To calculate: To prove that the differential equation $\frac{dy}{dt}=f(y)$ has the constant function y₂(t)=y_o is a solution. That is, y₂(t) is an equilibrium solution.

(d)

To determine

To calculate: To prove that y₁(t)=y₀ for all t.

(e)

To determine

To calculate: To prove that the solution of $\frac{dy}{dt}=f(y)$ has local minimum then it is a constant function that corresponds to an equilibrium solution.