I haven't checked if this is correct or not, but hope it helps:
sage: t = var('t')
sage: x = function('x', t)
sage: de = lambda y: diff(y,t,t) + (1-I)*diff(y,t) - I*y
sage: desolve(de(x(t)),[x,t])
'%e^((%i-1)*t/2)*(%k1*sin(sqrt(-4*%i-(1-%i)^2)*t/2)+%k2*cos(sqrt(-4*%i-(1-%i)^2)*t/2))'
On Fri, Mar 28, 2008 at 12:04 PM, Jim Clark
<[EMAIL PROTECTED]> wrote:
>
> Thanks for the help provided so far, but I have encountered a new
> problem that I've been unable to solve: a second-order DE with
> constant but *complex* coefficients:
>
> y'' + (1 - i)y' - iy = 0
>
> sage: maxima.de_solve('derivative(y,x,2) + (1 - i) * derivative(y,x)
> - i * y = 0', ['x','y'])
>
> yields:
>
> Exception (click to the left for traceback):
> ...
> Is i+1 zero or nonzero?
>
> Looking at the maxima documentation, there appears to be a way to
> tell maxima maxima.assume('i+1 <> 0'), but this syntax seems to send
> sage into the ozone.
>
> Thanks in advance for help offered.
> Jim Clark
>
>
> On Mar 21, 2008, at 5:29 PM, David Joyner wrote:
> >
>
> > If your main interest is in solving DEs using SAGE, then you might be
> > interested in the material on
> > http://sage.math.washington.edu/home/wdj/teaching/index.html
> > You may also be interested in joining sage-edu, which is
> > unfortunately not on http://www.sagemath.org/lists.html
> > but can be found here: http://groups.google.com/group/sage-edu
> >
> >
> > On Fri, Mar 21, 2008 at 5:15 PM, Jim Clark
> > <[EMAIL PROTECTED]> wrote:
> >> Hello SAGE people:
> >>
> >> I want to report a problem I encountered in my attempts to learn
> >> SAGE
> >> via the tutorial.
> >>
> >> First of all, I installed SAGE on my home computer, an iMac with
> >> OS X
> >> 10.4.
> >>
> >> I have been running the documentation by way of the "help" link in
> >> the notebook.
> >>
> >> When I came to differential equations, this is what I saw on my
> >> screen:
> >>
> >>
> >>>
> >>
> >>
> >>
>
>
> >> This was puzzling, to say the least. (It has taken quite a bit of
> >> effort to discover how to solve simple differential equations...)
> >>
> >> Along the way I decided to check out the documentation from the
> >> sagemath.org home page. The tutorial is presented differently. The
> >> same example appears:
> >>
> >>
> >>
> >>
> >> It made a lot more sense when I could see the equations!
> >>
> >> Has this problem with the "live" tutorial been recorded? Is someone
> >> working on it?
> >>
> >> I also have an opinion: This example is much too complicated for the
> >> tutorial. I think the tutorial should first present a single, simple
> >> DE before diving into systems of DEs.
> >>
> >> Furthermore, I have an additional gripe, coming into SAGE with no
> >> knowledge whatsoever of the systems that SAGE is built upon. It
> >> appears that solving differential equations depends on something
> >> called maxima, about which I initially knew nothing (a Google search
> >> has now taught me a bit about what it is, but it appears that if I
> >> want to solve differential equations, then I must learn maxima in
> >> addition to SAGE.)
> >>
> >> At any rate, I would have found it helpful in the tutorial if there
> >> were a bit of explanation of this relationship of SAGE to the
> >> various
> >> subsystems, perhaps with tables showing which subsystems do what,
> >> when one needs to be explicit about invoking the subsystem and how
> >> one goes about such invocation from SAGE.
> >>
> >> At any rate, thanks for all you are doing. I hope that, by sharing
> >> the difficulties I have encountered coming into SAGE completely
> >> cold,
> >> you will be able to improve your product.
> >>
> >> Jim Clark
> >>
> >>
> >>
> >
> > >
>
>
> >
>
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