Given:

$\{$:$[\frac{d{x}_1}{dt}=999x_1+1999x_2],[\frac{d{x}_2}{dt}=-1000x_1-2000x_2]\}{x}_1(0)=x_2(0)=1$

a$.$ Determine the stability of the above differential equation in time domain.

b$.$ Write a MATLAB script file to solve the above differential equation with $($a$)$ Explicit and $($b$)$

implicit Euler methods $($c$)$ Trapezoidal method and $($d$)$ Adams$-$Moulton method

Use step size $=0\mathrm{.}005s,$ and plot $x_1(t)$ and $x_2(t)V_s$ time $($in sec$)$ in a singlegraph from $t=0$ to

$0\mathrm{.}2s.$