As preparation for project one, solve the following boundary value problems in MATLAB $($or python$)$ using the two element approximation with nodes at $x=0,x=\frac{1}{2},$ and $x=1.$ For each one, plot your numerical solution along with the exact solution.

a$.u_1-3=0$

$u(0)=1$

$u(1)=0$

b$.u_{,}-x=0$

$u(0)=1$

$u_{,x}(1)=1$

c$.u_{,}-3x=0$

$u_{}(0)=2$

$u(1)=0$

Note: If you are looking for more practice for midterm $1,$ you can solve b and c above following the format in problem $2.$