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ODE with complex coefficients
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Virgil Stokes  
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 More options 7 Nov, 11:55
Newsgroups: comp.soft-sys.math.mathematica
From: Virgil Stokes <v...@it.uu.se>
Date: Sat, 7 Nov 2009 11:55:14 +0000 (UTC)
Local: Sat 7 Nov 2009 11:55
Subject: ODE with complex coefficients
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Does anyone have an example of a 1st order ordinary differential
equation (initial condition type) with complex coefficients that can
have oscillations?

--V. Stokes


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Mark McClure  
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 More options 8 Nov, 11:50
Newsgroups: comp.soft-sys.math.mathematica
From: Mark McClure <mcmcc...@unca.edu>
Date: Sun, 8 Nov 2009 11:50:54 +0000 (UTC)
Local: Sun 8 Nov 2009 11:50
Subject: Re: ODE with complex coefficients
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On Sat, Nov 7, 2009 at 6:50 AM, Virgil Stokes <v...@it.uu.se> wrote:
> Does anyone have an example of a 1st order ordinary differential
> equation (initial condition type) with complex coefficients that can
> have oscillations?

Does this count:
Clear[y];
{sol} = DSolve[{y'[t] == I*y[t], y[0] == 1},
   y[t], t];
y[t_] = y[t] /. sol;
y[t] // InputForm
E^(I*t)

We could visualize it like so:
Graphics3D[Line[Table[{t, Re[y[t]], Im[y[t]]},
   {t, 0, 20, 0.1}]]]

Mark McClure


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