Required calculations:

$(15$ points$)-$Using MATLAB, solve for $T_1,T_2,T_3,$ and $T_4.$

$(15$ points$)-$Using MATLAB, develop a plot of temperature $)$ ranging from $40$ to $200$ vs $.$ distance $(x,m)$ along heated rod to $x=10$ at step size $x=2.$

$(15$ points$)-$Using EXCEL and Equation $(2),$ develop a plot of $T(C)$ vs$.x(m)$ with step size $x=1.$

NOTE: The details of your MATLAB program with plot, EXCEL table with plot is required for full credits.

$2.(45$ points$)-$Write a MATLAB Code to solve the following first$-$order ODE using classical fourth order Runge$-$Kutta method.

$\frac{dy}{dx}=3e^{-x}-0\mathrm{.}4y$ from $x=0$ to $x=4\mathrm{.}5$ with initial condition $y=5$ at $x=0$ using a step size of $h=1\mathrm{.}5$

Required calculations:

$(20$ points$)-$Using MATLAB, solve $k_1,k_2,k_3,$ and $k_4$ for each iteration $($total of $3$ iterations$)$

$(20$ points$)-$Using MATLAB, develop a plot of $y$ vs$.x$ with $0\mathrm{.}5$ increment.

$(5$ points$)-$Using EXCEL, summarize your work $(x,y,$ and $k-$values$)$ in a table.

NOTE: The details of your MATLAB program with plot, table of $(x,y,$ and k $-$values$)$ are required for full credits.

$3.$ NEATNESS $(10$ points$)!$ No screen shot! Attach this sheet to your file's printout.