In this question, you will explore some basic commands in MATLAB. Consider the IVP

$\frac{dy}{dx}=e^{2x}+y,y(0)=-1$

We want to find and approximate solution on $0,0\mathrm{.}3$ using Euler's Method with

step size $h=0\mathrm{.}1.$

Hint: Euler's method has the formula $y_{i+1}=y_i+h*f(x_i,y_i).$ We will define the

function $f$ using the command:

$>>f=$@$(x,y)e^{2x}+y$

put the $x-$values $,$ and $0\mathrm{.}3$

$($a$)$ Try the followings in the command window of MATLAB, and explain what

these commands do:

$>>a=9$

$>>b=\frac{}{6}$

$>>c=5*sin(b)-\sqrt[\phantom{2}]{a}$

$>>d=$exp$(2)$

$>>e=log(d)$

$($b$)$ In MATLAB, we can define and plot a function $y=x^3+x^2+x+1$ on the

interval $0,5$ using the following commands:

$>>f=$@$(x)x.{?}^3+x.{?}^2+x+1$

$>>x=0$:$0\mathrm{.}1$:$5$

$>>y=f(x)$

$>>$plot$(x,y)$

Explanation:

$(1).$ Define the function using the function handle in MATLAB.

$(2).$ Pick descrete $x-$values on $0,5$ with increment $0\mathrm{.}1.$

$(3).$ Compute the corresponding $y-$values.

$(4).$ Use the plot command to draw the graph.

Please modify the commands and use them to plot the function $y=e^x+xcosx$

on $0,3.($Make sure to include this figure in your report.$)$