1. Write a. function van_der_pol which takes input parameters mu, x0, and ti and plots the solution of the Van der Pol equation in the phase plane (is. plots the trajectory :J:{t) versus m'[t) in the mm' plane). The Van der Pol equation is with parameter p. dened by mu, initial conditions given by at) (a Python list of length 2), and the plot is for t in the interval [(Ltf] (where if is given by tf). 2. Write a function called pendulum which takes input parameters L, theta and ti, and plots the solution Hft) of the simple pendulum equation it?!) 9 _ EJ'E'L\" where g is aeoeleration of gravity (9' = 931 mfsz), L is the length of the pendulum measured in metersI initial conditions given by theta (a. Python list of length 2], and the plot is for t in the interval [0,tf] [where t; is given by tf}. 4. 1Write a function called trig_ode 1which takes input parameters alpha, beta, 3C! and tf [in that order and with default values; a1pha=1, beta=1, y= and tf=1), and which plots the solution of the equation y' = sin'iur} + maiii} r rm) = 5"\" over the interval [[11 15;] where t; = tf, and where o: = alpha and = beta