Consider the following MATLAB commands

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

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

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

$>>$ 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.