1. (a) Modify the function ex with 2eqs to solve the IVP (L4.4) for 0 t 40 using the MATLAB routine ode45. Call the new function LAB04ex1. Let [t,Y] (note the upper case Y) be the output of ode45 and y and v the unknown functions. Use the following commands to define the ODE: function dYdt= f(t,Y) y=Y(1); v=Y(2); dYdt = [v; cos(t)-4*v-3*y]; Plot y(t) and v(t) in the same window (do not use subplot), and the phase plot showing v vs y in a separate window. Add a legend to the first plot. (Note: to display v(t) = y (t), use v(t)=y(t)). Add a grid. Use the command ylim([-1.5,1.5]) to adjust the y-limits for both plots. Adjust the x-limits in the phase plot so as to reproduce the pictures in Figure L4g. Include the M-file in your report.

1.5 0.5 -0.5 0.8-06 -04 -02 0.2 0.4 0.6 0.8 10 15 20 25 40 Figure L4g: Time series y-y(t) and v-u(t)-y'(t) (left), and phase plot u-y, vs. y for (L44) (b) For what (approximate) value(s) of t does y reach a local maximum in the window 0