Problem $4$: Numerical Methods $($Shooting Method$)(25$ Points$)$

Your goal is to calculate the temperature profile within a rectangular fin for the following conditions. The governing equation is given by:

$\frac{d^{2}T}{d{x}^2}=A(T-300)$

The specified temperatures at either ends of this $0\mathrm{.}1$ m long fin are:

$T(0)=1000K$

$T(0\mathrm{.}1)=300K$

Use the following values for the constant A in the differential equation above:

a$.$ Dividing your fin into a number of equally spaced segments $($of your choice$),$ and use the shooting method to get the temperature profile within the rectangular fin. Report your values in a table $($an example format with made up numbers is given below$)(10$ points$)$

$\backslash$table$[[x(m),T(x)$ in $K$