For the following differential equation: $(1/$a$)$u$"-$u$\text{'}+1=0,$ for $0<=$ x $<=1$ with boundary conditions u$(0)=1$ and u$(1)=4$ Develop:

$($a$)(10$ pts$)$ Consider a regular mesh whose distance between nodes is h $=0\mathrm{.}2,$ find the equation

discrete differential for an internal node i

$($b$)(10$ pts$)$ Write the entire system of equations corresponding to the system. Include the equations for the boundary conditions.

c$)(5$ pts$)$ Write the system of equations as a matrix system Ax $=$ b$.$

$(($d$)(5$ pts$)$ Solve the matrix system with Matlab and write your result by hand.