***THESE QUESTIONS ARE FOR MATLAB***

A classical ODE system can be described by three odes. The equations are x=(y-x) Here , r, b are all positive parameters. Consider the scenario that =10, b=8/3, r-28. 1. Solve this ODE. Use tspan= [0 50]. (4pt) Initial condition (0,1,0) Initial condition (0,1.0001, 0) a. b. 2. Plot "x vs t", "y vst" and "z vs t" (2pt) Use subplot to show 3 plots in one figure. Label axis. Plot corresponding solutions in the same plot (i.e. plot "x vs t" from both initial conditions in the same plot and so on) Describe what you see in the comment. How significant is the initial condition? Is the solution linear or nonlinear? a. b. 3. In a new figure, plot "x vs y vs z"of solution from 1.(a) in 3D. Label axis. (1pt) Look up "chaos attractor" in Wikipedia. Find the name of this ODE system and indicate it in the title of the figure. a