On Friday, February 20, 2015 at 9:15:29 AM UTC-8, Ralf Stephan wrote:
>
> Hello,
> I'm puzzled about
>
> sage: var('a,t')
> sage: y = function('y')(t)
> sage: desolve(diff(y,t)-(2*t*y-6/t-6/t^3), y).simplify_full()
> _C*e^(t^2) - 3*Ei(-t^2)*e^(t^2) + 3*e^(t^2)*gamma(-1, t^2)
>
> because c*e^(t^2)+3/t^2 is (also?) a solution to this ODE according to
> Wolfram.
> So, is the second solution a simplification of the first (and so this a
> bug in Maxima),
> or are both solutions valid (meaning perhaps they are both not the general
> one?)?
>
> Regards,
>
It does look like:
(-3*Ei(-t^2)*e^(t^2) + 3*e^(t^2)*gamma(-1, t^2) - 3/t^2) / (e^(t^2))
is awfully close to being constant (in fact, identically zero outside t=0),
and indeed there are all manner of interesting identities relating the
exponential integral and the incomplete gamma function. So I think Wolfram
and Maxima are in agreement on this one (although Wolfram produces a
perhaps preferable form for the answer)
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