Consider the differential equation where a and b are positive constants. (a) Either...

Consider the differential equation where a and b are positive constants.

(a) Either by inspection or by the method suggested in Problems 33– 36, find two constant solutions of the DE.

(b) Using only the differential equation, find intervals on the y-axis on which a nonconstant solution is increasing. Find intervals on which is decreasing.

(c) Using only the differential equation, explain why is the y-coordinate of a point of inflection of the graph of a nonconstant solution

(d) On the same coordinate axes, sketch the graphs of the two constant solutions found in part (a). These constant solutions partition the xy-plane into three regions. In each region, sketch the graph of a nonconstant solution whose shape is suggested by the results in parts (b) and (c).