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Re: InverseLaplaceTransform different solution in Mathematica 6 and

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94171] Re: InverseLaplaceTransform different solution in Mathematica 6 and
  • From: dimitris <dimmechan at yahoo.com>
  • Date: Sat, 6 Dec 2008 06:16:12 -0500 (EST)
  • References: <gh8hnh$r3o$1@smc.vnet.net>

On 4 =C4=E5=EA, 14:16, Guillermo Sanchez <guillermo.sanc... at hotmail.com>
wrote:
> Dear friends,
> Mathematica 6 gives the analytical right answer evaluating
> InverseLaplaceTransform[E^((1 - Sqrt[1 + 4*d*(s + d*r)])/(2*d)), s,
> t],
> However Mathematica 7.0.0 does not the analytical solution. Is it a
> bug?
>
> Guillermo

Did you try to evaluate the inverse Laplace function for a specific
value of d?
Is d positive for example?
I don't own version 6, let alone 7 but the following "trick" used to
work in some
older versions...

In[254]:=
E^((1 - Sqrt[1 + 4*d*(s + d*r)])/(2*d)) /. d -> Catalan
InverseLaplaceTransform[%, s, t]
% /. Catalan -> d

Out[254]=
E^((1 - Sqrt[1 + 4*Catalan*(Catalan*r + s)])/(2*Catalan))

Out[255]=
E^(1/(2*Catalan) - 1/(4*Catalan*t) - t/(4*Catalan) - Catalan*r*t)/
(2*Sqrt[Catalan*Pi]*Sqrt[t^3])

Out[256]=
E^(1/(2*d) - 1/(4*d*t) - t/(4*d) - d*r*t)/(2*Sqrt[d]*Sqrt[Pi]*Sqrt
[t^3])

Regards
Dimitris


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