Solve the following ODE through python (jupyter): d²y/dx² = -1001*dy/dx-1000*y with initial conditions y(0) = 1 and y'(0) = 0.

(a) Solve this ODE in the region from x = 0 to x = 5 analytically and numerically using the explicit Euler method, Heuns method, the midpoint method, and the implicit Euler method.

(b) Investigate what values of the stepsize yield accurate results for these methods. How does the global error decrease with the stepsize for each method?

(c) Investigate what values of the stepsize yield stable and unstable solution. Analyze your results both graphically and quantitatively.