2010/3/22 YURi KARADZhOV <yuri.karadz...@gmail.com>:
> I played around with sage and found some problems with desolve command.
> To solve ode diff(y(x),x)+a*y(x)+b*x+c we should first define variables and
> functions
>
> x = var('x')
>
> a,b,c=var('a b c')
>
> y=function('y',x)
>
> eq=diff(y,x)+a*y+b*x+c
>
> but than unless it is obvious that the dependent variable is x and
> independent is y we should write such command
>
> desolve(eq,y,ivar=x)
>
> which is really annoying. And what is worse - we get a wrong answer
>
> -((a*x - 1)*b*e^(a*x)/a^2 + c*e^(a*x)/a - c)*e^(-a*x)
>
> but the right answer is
>
> -((a*x - 1)*b*e^(a*x)/a^2 + c*e^(a*x)/a - _C1)*e^(-a*x)
>
> where _C1 - arbitrary constant.
>
> Of course, if we don't use c as a variable in equation we will get a right
> answer, but another problem will rise. If we have a bunch of ODE and want
> their solutions to interact somehow, than we expect different arbitrary
> constant for each one. But sage uses one letter c in every solution, which
> causes problems.
>
>
> Actually the first problem is easy to solve.
You should implement the change and post a patch to
http://trac.sagemath.org/sage_trac/
for review. That's how Sage development happens. Hundreds of people
have done this. It's like notices a problem in a wikipedia article,
and fixing it.
Thanks!
William
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