1. Draw phase diagrams for the following ODEs: (a) (5 marks) dy = 1 2 - 2 dt (b) (5 marks) dy dt = y(3 - y)(25 - 42) 2. Find the equilibria for the differential equations and determine the values of a for which each equilibrium is locally stable. Assume a # 0. (a) (5 marks) dy =1-e-ay dt (b) (5 marks) dy = y(a - y) 3. Find and classify all equilibria of the following ODEs and plot their phase diagrams: (a) (5 marks) 29 = y + 2ylny (b) (5 marks) ay = 3y - ye-" dt