2. (15 points) Consider the following logistic equation initial value problem: dy 1 y = 1) 0: 20,190. (i) (2 points) Sketch the righthand side of the equation as a function of 3;. (ii) (2 points) Determine the intervals of y in which 3; is increasing. and those in which y is decreasing. Hint: Use the rst derivative test. (iii) (2 points) Determine the intervals of y in which y is concave up or concave down. Hint: Use the second derivative test and the chain rule. (iv) (2 points) Use the information you extracted in parts (i)-(iii) to sketch the inte- gral curves (i.e. solutions) corresponding to yo : 1. yo : 3. yo : 6 and yo : 8. (v) (2 points) Use your sketch in part (iv) to classify the equilibria (if any) of the equation as either asymptotically stable (solution curves approaching the equilibrium curve as t a 00) or unstable (solution curves departing from the equilibrium curve as t > 00). (vi) (5 points) Obtain a formula for the solution of the initial value problem for any 90