Assignment 4 Due February 26 Computer Assignment This is an assignment to use three computer programs. If you do not know a computer program that takes roots of polynomials, go to the help section of matlab (or whatever you are using). pplane is a program of matlab very similar to dfield. To use it, you must convert the second order equation into a system. ode45 is another program of matlab...you can, of course, use any ode solver that will give you output as graphs. There is a help sheet on ode45 on the home page for the course. 1.Use a computer program to find the roots of the equation r^4 +5r^3 +7r^2 +5r +1. Now give the general solution to the equation y'''' + 5y''' + 7y'' + 5y' + y = 0. 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 most solutions as t goes to + infinity? Be as specific as you can be. 3. Consider the equation x" + 5x' + 4x = 0. Use pplane to make a graph. What happens to most 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(1.2t). (Meaningful means that you have set the time limits and chosen fairly typical initial conditionsappropriately so that you see what is happenning). 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' = 2N(-1 + M/10). Make both a pplane plot and an ode45 plot of the solution with M(0) = 1, N(0) = 1.