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From: Virgil Stokes on 7 Nov 2009 06:55
Does anyone have an example of a 1st order ordinary differential
equation (initial condition type) with complex coefficients that can
have oscillations?

--V. Stokes


From: Mark McClure on 8 Nov 2009 06:50
On Sat, Nov 7, 2009 at 6:50 AM, Virgil Stokes <vs(a)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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