I don't. I get an error that Sage simply can't solve the equation:
{{{
reset()
var('t, k')
x2=function('x2',t)
x1=function('x1',t)
#and then i am trying to solve the following system
solve([x1==integral(x2), k*x1+diff(x2,t)==0],diff(x1,t),diff(x2,t))
///
...
ValueError: Unable to solve [x1(t) == integrate(x2(t), t), diff(x2(t),
t, 1) + k*x1(t) == 0] for (diff(x1(t), t, 1), diff(x2(t), t, 1))
}}}
> I guess that the reason for this is that
> diff((x1==integral(x2)),t)
That expression isn't in your input.
... Anyway, what I wish I could do is show how to solve your problem
using Sage, but unfortunately I have to do some other things right now...
>
> returns with the same output message
> Exception (click to the left for traceback):
> ...
> TypeError: cannot coerce type '<class
> 'sage.calculus.equations.SymbolicEquation'>' into a
> SymbolicExpression.
>
>
> even though that
> diff(integral(x2),t) returns with x2.
>
> So i am wondering, is there a way to force sage to differentiate a
> symbolic expression?
> MTIA
>
> >
>
--
William Stein
Associate Professor of Mathematics
University of Washington
http://wstein.org