Timothy C. answered • 03/18/19

Mathematics Professor with over 20 Years of Teaching Experience

(a) Constant solutions, also called equilibrium solutions, satisfy dy/dx=0.

If we factor the right-hand side of the equation, we have

dy/dx = y^{2}(y-1)(y-3). Setting the right-hand side equal to zero, we obtain the constant solutions y=0, y=1, y=3.

(b) Solutions are increasing when dy/dx > 0. Note that dy/dx > 0 for the set of y values (-∞,0) ∪ (0,1) ∪ (3,∞) Hence solutions are increasing when y in is the set (-∞,0) ∪ (0,1) ∪ (3,∞) .

(c) Solutions are decreasing when dy/dx < 0, and dy/dx < 0 when 1 < y < 3. That is, solutions are decreasing when y is in the set (1,3).