Cross posted in Mathematica.SE, I'll try to rephrase it in a more general way here.A friend of mine showed me this initial value problem (IVP) for a linear ordinary differential equation (ODE) with variable coefficient:$$y''(x)=\left(x^2-1\right) y(x)$$$$y(0)=1$$$$y'(0)=0$$Seems to be a simple one, right? Actually it can be solved analytically and the solution is:$$y(x)=e^{-\frac{x^2}{2}}$$But when I tried to solve it with the classical RungeKutta method, the numerical solution blows up:The step size used here is 0.001.Why did this happen? If I've chosen an improper method, what's a suitable one? 
Numerical solution of IVP for linear ODE with variable coefficient blows up
ode;stability;time integration