Mathlab :

Problem $2$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$ Slopefieldicym $x+$

$[x,y]=$ meshgrid $(0$:$\mathrm{.}5$:$8\mathrm{.}0,-3$:$0\mathrm{.}5$:$9\mathrm{.}0)$;

G Figure $1$

slope $=y{*}^{**}(1-\frac{y}{4})$;

File ted View insert Toels Desitop Window Help

Length$=$sqrt $(12)$

UnitVectorx$=1./$Length;

UnitVectory$=$slope.$/$Length;

quiver $(x,y,$ UnitVectorx, UnitVectory$)$

Command WindowClick on New or the $+$ sign.In the Edit Window Type in the Script, the name of the Script will be untitled$1.$Save the Script and Give it a name.Run the name of the Script in the Command Window.The SlopeField should be come up a NewWindow as shown.G$.$ Carbone$4$Use MATLAB to generated the direction field for following autonomous differential equation.

$\frac{dy}{dx}=y(1-\mathrm{.}25y),$ You can use the script below. Print out the direction field or take a picture with your smart phone. Hand draw the solutions to the differential equation for the following initial conditions:

$y(0)=8$

$y(0)=0\mathrm{.}1$

$y(0)=-0\mathrm{.}1$