Part I. WITH Calculator Consider the logistic differential equation = 10y - - with y(0) = 2. (1) Show that the given differential equation is equivalent to ~= 10y (1 -). (0.5 pt.) (2) Find the particular solution to the differential equation using the method of separation of variables with partial fraction decomposition . Show all necessary steps in your work . (4 pts.) (3) The particular solution to the given differential equation is a sigmoid. Find the coordinates of the point of inflection of this sigmoid. (1 pt.) (4) Find the equation of the stable equilibrium solution to the differential equation. (1 pt.) (5) Assume that the given differential equation represents the growth of population of an endangered species over time t in years. Algebraically find the time at which the population equals 25? (1 pt.) (6) If Euler's Method is used to approximate y(0.5), will the approximation be an underestimate or an overestimate of the expected value? Justify your answer. (1 pt.)