Numeric approxiamtions

Or, we could have Mathematica do all the nasty approximations behind our backs and use NDSolve:

This error message is a warning that you can't trust this approximation beyond about .  To fix that, you must increase the maximum number of steps (which will take longer to compute):

Now, as before:

You had better pay attention to this warning.  What is the problem?  We told NDSolve to solve on the domain , not for negative t.  This is something you need to watch out for.