Solve the two$-$point boundary value problem

${}^{\text{'}\text{'}}+2x{u}^{\text{'}}-x^{2}u=x^2,u(0)=1,u(1)=0$

lumerically using finite differences. Use the lowest$-$order centered finite$-$difference approximations for $u^{\text{'}}$ and $u^{\text{'}\text{'}}($formulas are below$).$ Take $n=10$ equally spaced subintervals on

$c_0=0x1=x_n.$

Call your solution vector $u.$ It should be an $111$ column vector containing $u(x_0),u(x_1),$dots,$u(x_n).$ Then, make a plot of the function $u(x).$

Lowest$-$order finite difference approximations:

First derivative:

Second derivative: