Assignment 5 1. Consider the differential equation y" + by' + y = 0. Identify the values of b for which the roots are complex the values of b for which the roots are realand. Choose a value for b from each of these ranges and make two computer graphs using ode45 with y(0) = 1 and y'(0) = 0. Explain the difference. 2.Consider the equation x" + 5x'- 6x = 0. Use pplane to make a graph of the x(t), x'(t) curve in phase space. Plot a few typical solutions. What happens to solutions as t goes to + infinity? 3. Consider the equation x" + 5x' + 4x = 0. Use pplane to make a graph. What happens to solutions as t goes to infinity? Where do solutions come from if you look back to - infinity? 4. Make a meaningful ode45 plot of a solution to the equation x" + x = sin(1.1t). Explain how it illustrates what we did in class. 5.A basic preditor-prey system for the population of preditors N and prey M has the form (the constants are somewhat arbitrary) M' = M(5 - M/10 - N) N' = N(-1 + M/10). Determine using pplane what this system does in the first quadrant (it doesn't make sense to talk about negative populations). Find the equilibrium solutions. This will help you set the paramters. We will learn how to analyze such systems after we have studied matrices.