c$)$ Discretize the ODE systems using the finite difference method. In this regard, divide the time window of $10$s uniform time intervals $\backslash$Delta t $=2$s and discretize the ODE system and come up with a linear system of equation as a matrix $$ vector equation.

Write a Matlab code that solves numerically for the same problem. i$)$ Use $\backslash$Delta t $=0\mathrm{.}6$s and plot the numerical solutions u$1$ & u$2$ with the analytical solutions in the same figure. ii$)$ Use $\backslash$Delta t $=0\mathrm{.}06$s and plot the numerical solutions u$1$ & u$2$ with the analytical solutions in the same figure.