Code To Be Modified

$\%$ Code for Logistic Slope Field with Solutions.

$r=0\mathrm{.}5$; Kgrowth rate

$K=10$; $\%$Carrying capacity

$t=[0$:$0*2$:$20]$;$\%$ vector for time

$\%$ Define the values of $x$ and $y$ that we will use to create the slope field $\%$ we use $ts$ and ps to identify the values of time and population $\%$ to be used for slope field.

$[ts,pS]=$ meshgrid $,$;

$\%$ Define the values of the slope $(p^{\text{'}})$

$s=,$;

$\%$ The following line is needed to find the size of each vector $(1,5)$ so $\%$ that we can scale all of the arrows to have the same magnitude $=1$

$L=\sqrt[\phantom{2}]{1+s{*}^{{?}^{?}}2}$;

figure$(2)$

hold on $\%$this command tell MATLAB to draw everything on the current figure quiver$($tS$,$ pS$,\frac{1.}{L},S\frac{.}{L},0\mathrm{.}5),$ axis tight

xlabel $(\text{'}$time$\text{'})$;

ylabel$(\text{'}$population$\text{'})$;

title$(\text{'}$Direction field for $($:$d\frac{p}{d}t=r^{**}{p}^{**}(1-\frac{p}{K}{)}^{\text{'}}\}$;

$\%$ The nex part adds the solution curves to the slope field

$\%$ there are $3$ meaningful cases which we will draw in red, green, magenta

po:

$p=$

plot$(t,p,{?}^{\text{'}}{g}^{\text{'}})$

$p0=K_j$

$p=$

plot$(t,p,{?}^{\text{'}}{r}^{\text{'}})$

$p=5$;

$p$ :

plot$(t,p,{?}^{\text{'}}{m}^{\text{'}})$

hold off $\%$this command tell MATLAB to stop drawing on figure