desolve cannot solve some differential equations that ode2 can?

Hi,

I'm trying to solve a system of equations that can be written as:

eqn1: %i * 'diff(a(t),t) = exp(%i * d * t) * b(t);
eqn2: %i * 'diff(b(t),t) = exp(-%i * d * t) * a(t);

But trying to solve it using desolve tells me desolve cannot solve it:

(%i27) desolve([eqn1, eqn2],[a(t),b(t)]);

`algsys' cannot solve - system too complicated.
`desolve' can't handle this case.
 -- an error.  Quitting.  To debug this try debugmode(true);

However, if I rewrite as second-order differential equations (assuming
I didn't make a mistake ;) ), as:

eqn1: 'diff(a,t,2) - %i * d * 'diff(a,t) + a = 0;
eqn2: 'diff(b,t,2) + %i * d * 'diff(b,t) + b = 0;

and solve them separately using ode2, I get an answer (and seems to
agree with what I get when I solve the system of first-order equations
above, using the commercial derivative of Macsyma, up to a constant).

I'm wondering---is this difference typical? And, in general, should I
expect desolve to be less powerful than ode2, or is there something
special I can do with desolve to try to make it solve this particular
problem?

I thought I'd ask, since this seemed like it could be a little
problematic for me, esp. in the future if I come across system of
differential equations that I can't separate using only second-order
forms.

Thanks,

Andrzej

P.S. I found a similar discussion at
http://article.gmane.org/gmane.comp.mathematics.maxima.general/1651/,
but I was hoping there was some improvement in the intervening few
years.

P.S. I'm using Maxima version 5.10 (included in Debian Etch stable).