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Re: ODE with complex coefficients

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104743] Re: [mg104712] ODE with complex coefficients
  • From: Mark McClure <mcmcclur at unca.edu>
  • Date: Sun, 8 Nov 2009 06:48:47 -0500 (EST)
  • References: <200911071150.GAA10178@smc.vnet.net>

On Sat, Nov 7, 2009 at 6:50 AM, Virgil Stokes <vs at 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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