Now consider the boundary value problem for an ODE that describes the temperature of an object that ranges from $x=0$ to $x=1$ in one spatial dimension:

$de{l}^2\frac{T}{\frac{?}{?}}del{x}^2=-\frac{x}{\frac{?}{?}}k$

Subject to the following boundary conditions:

$T(0)=0$

$T(1)=1$

Where $k$ is a constant for conductivity. Create a function called solve BVP FD$()$ that will use the central finite difference method as in $P1,$ and as seen in class.

The function should take the following input in the following order:

float TO: Temperature at left boundary

float T$1$: Temperature at right boundary

float $k$ : The coefficient that shows up in the equation

int $dx$ : The desired spacing for the finite difference approximation

and outputs in the following order:$*$ numpy vector $T$ : The estimated solution $T$ at each point in space $x=0,dx,2dx,$dots,$1$

Hint: This example also has an analytic solution of the form:

$T(x)=-\frac{x^3}{6}k+(1+\frac{1}{6}k)x$

you can use a value with $k=0\mathrm{.}1$ in this case, your finite difference solution should be very close to the true solution since the true solution is just a cubic function.