Q$.($Numerical analysis$)$ The axial temperature variation of a current$-$carrying bare wire is described by:

$\frac{d^{2}T}{d{x}^2}-\frac{4h}{kD}(T-T_{})-\frac{4{}_{SB}(T^4-T_{}^4)}{kD}=-\frac{I^2{}_e}{k(\frac{1}{4}{D}^2{)}^2}$

where $T$ is the temperature in $K,x$ is the coordinate along the wire, $k=72\frac{W}{m}\frac{?}{K}$ is the thermal conductivity, $h=2000\frac{W}{m^2}\frac{?}{K^2}$ is the convective heat coefficient, $=0\mathrm{.}1$ is the radiative emissivity, ${}_{SB}=5\mathrm{.}67{10}^{-8}\frac{W}{m^2}\frac{?}{K^4}$ is the Stefan$-$Boltzmann constant, $I=2A$ is the current, ${}_e=32{10}^{-8}m$ is the electrical resistivity, $T_{}=300K$ is the ambient temperature, $D=7\mathrm{.}62{10}^{-5}m$ is the wire diameter, and $L=4\mathrm{.}0{10}^{-3}$ is the length of the wire. The boundary conditions are:

$atx=0,T=300K,$ and $atx=\frac{L}{2},\frac{dT}{dx}=0$

$*$Use MATLAB's built$-$in function bvp $4$ c to solve the boundary value problem for $0x\frac{L}{2},$ since the temperature distribution is symmetric about $x=\frac{L}{2}.$ Plot the temperature distribution along the wire.$*$