Chapter 26, Problem 14P

Given the first-order ODE

$\begin{array}{l}\frac{dx}{dt}=-700x-1000e^{-t}\\ x\left(t=0\right)=4\end{array}$

Solve this stiff differential equation using a numerical method over the time period $0\le t\le 5$. Also solve analytically and plot the analytic and numerical solution for both the fast transient and slow transition phase of the timescale.