Chapter 26, Problem 15P

The following second-order ODE is considered to be stiff

$\frac{d^{2}y}{d{x}^2}=-1001\frac{dy}{dt}-1000y$

Solve this differential equation (a) analytically and (b) numerically for $x=0\text{ to }5$. For (b) use an implicit approach with $h=0.5$. Note that the initial conditions are $y\left(0\right)=1$ and $y^{\prime }\left(0\right)=0$. Display both results graphically.