Write a function M$-$file that implements $(8)$ in the interval $0t55.$ Note that the initial

condition must now be in the form $y0,v0,w0$ and the matrix $Y,$ output of ode$45,$ has now three

columns $($from which $y,v$ and $w$ must be extracted$).$ On the same figure, plot the three time series

and, on a separate window, plot the phase plot using

figure$(2)$; plot$3(y,v,w)$;

hold on; view $(-40,60)$

xlabel$(\text{'}$y$\text{'})$; ylabel$(\text{'}$v$=$y$\text{'}\text{'}\text{'})$; zlabel$(\text{'}$w$=$y$\text{'}\text{'}\text{'}\text{'}\text{'})$;

Do not forget to modify the function defining the ODE.

The output is shown in Figure $9.$ The limits in the vertical axis of the plot on the left were delib$-$

erately set to the same ones as in Figure $8$ for comparison purposes, using the MATLAB command

$y\underset{?}{lim}([-2\mathrm{.}8,2\mathrm{.}8]).$

You can play around with the $3$D phase plot, rotating it by clicking on the circular arrow button

in the figure toolbar, but submit the plot with the view value view $(-40,60]($that is$,$ azimuth

$=-40,$ elevation $=60).$