3. (28 pts) Consider the equation: dy = ( dt )2 3 -y)(y -1 Our goal is to compare the information that different methods of analysis give us. (a) (6 pts) What is the general implicit solution? (b) (4 pts) Now solve the equation using technology (e.g. Wolfram-Alpha, Desmos). What is the general solution? (c) (6 pts) Sketch (by hand) the phase diagram (NOT the slope field) for this differential equation. (d) (8 pts) What is the behavior of the solution asto for the initial conditions: (i) t 0, y 0, (ii) t 0, y-1, (iii) t 0, y-2, (iv) t 0,y-4. Which of the above analysis techniques did you use? d (8Du - 1) (e) (4 pts) Describe the different information we obtain by solving analytically from parts (a) and (b), and the phase diagram from part (c)