Consider the following MATLAB commands

$>[T,Y]=$ meshgrid$(-3$:$1$:$3,-3$:$1$:$3)$;

$>S=(Y+1{)}^{**}(1-Y)$;

$>L=\sqrt[\phantom{2}]{1+S.{?}^2}$;

$>$ quiver$(T,Y,\frac{1.}{L},S\frac{.}{L},0\mathrm{.}5),$ axis equal tight xlabel $\text{'}t\text{'},$ ylabel $\text{'}y\text{'}$;

$($a$)(10)$ What is the differential equation being studied?

$($b$)(10)$ Sketch the output of this code.