Thanks for the help, David.
The solution is quite simple: y = k1 e^(ix) + k2 e^(-x)
Needless to say, it is quite the algebraic challenge to verify that
sage's result (maxima's result?) is the same as this simple expression.
Jim
On Mar 28, 2008, at 9:17 AM, David Joyner wrote:
> 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
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