Can you please help answer these questions

Instructions Complete these Prop to completed ape Sheet of paper (or on a tablet/iPad). Your work should be neat and problems should be completed in the correct order. Submit the assignment as a PDF on Blackboard. Write down any intes or antiderivative that you evaluate to solve the equation. Show your sup- porting work if the integral requires simplification, substitution or integration by parts. If you use any method that is not covered in the notes/book, you must explain the method that you used provide a reference in order to receive credit. Problems 1. Consider y' = yes - 9y ey (a) Draw the phase diagram. Identify each equilibrium as stable or unstable. (b) Find lim y(t) for the solution that satisfies the initial condition: y(0) = 1 (c) Is it possible to find a value for yo such that the solution to the IVP: y' = yes - y ey y (0 ) = yo diverges to co as t - co? Why or why not? 2. A second order chemical reaction involves the interaction of one molecule of a substance P with one molecule of a substance Q to produce one molecule of a new substance X. We denote this by: P + Q - X Suppose that p and q, where p # q, are the initial concentrations of P and Q, respectively, and let x(t) be the concentration of X at time t. Then p - x(t) and q - x(t) are the concentrations of P and Q at time t, and the rate at which the reaction occurs is given by the equation: dx dt = a(p - 2)(9-2) where a > 0 is a constant. (a) Assume that 0