Consider the differential equation dy/dt = y(y − 1)(3 − y). (1) The solutions of this differential equation will have various behaviors that depend on an initial condition y(t0) = y0. We have considered how to sketch solutions for a differential equation of this form by making use of a plot of dy/dt versus y to plot the direction field (equivalently called the slope field) for this equation. We have also made use of the phase line to understand the behavior of the solutions near the steady states – places where dy/dt = 0. A) Identify the steady states of equation (1). Create a plot of dy/dt against y and label the steady states on this plot. Also, treat the horizontal axis as the phase line for this equation, and show the directions of flow for equation (1) on this phase line (the y-axis). B) For each steady state y = a, sketch the solutions y(t) of equation (1) for the set of initial conditions y(0) = a − 0.25, y(0) = a, and y(0) = a + 0.25. Use the same set of y versus t axes for sketching all the solutions together.