Using Matlab:

Write a script that finds a numerical solution to the second-order IVP x(t)'' (1 x^2 (t))x'(t) + x(t) A sin(t) = 0 using parameters = 8.53, A = 1.2, and = 2/10. Use the initial conditions x(0) = 2 and x 0 (0) = 0. (Note that the above equation reduces to the van der Pol equation we solved above if we set = 1 and A = 0. Adding in nonzero A adds forcing to the system, i.e. makes it non-homogeneous.) Plot for times t = 0 to t = 100. Include both a plot of x and v against time, as well as a phase space plot of your solutions. Plots should be appropriately labelled and titled. If you solve the system correctly, you will see some very strange behavior! In particular, there will be a pattern that almost repeats itself, but not exactly. This is an example of chaotic dynamics, which we will explore more thoroughly in a few weeks.