Sometimes a workaround is possible:
sage: x = var('x')
sage: y = function('y', x)
sage: C = var('C')
sage: f = desolve(diff(y,x) + y, y, ics=[0,C]); f
C*e^(-x)
sage: c = var('c')
sage: f = desolve(diff(y,x) +c*y, y,ivar=x, ics=[0,C]); f
C*e^(-c*x)
On Thursday, July 26, 2012 12:37:56 PM UTC+2, Nasser M. Abbasi wrote:
>
> I do not know much of anything about sage. But I was using desolve on
> http://www.sagenb.org to compare an answer,
> and I am confused on the type-setting of of constant of integration in
> solution of an ode.
>
> Googled around but nothing specific I could find.
>
> When I ask sage to solve an ode using desolve, it seems to use `c` for
> constant of integration in the result, like this:
>
> reset()
> x= var('x')
> y = function('y', x)
> desolve(diff(y,x)+y, y,ivar=x)
>
> which gives
>
> c*e^(-x)
>
> I wish it generated at least uppercase `C` or such. But any way. Now the
> confusing part.
>
> If I use `c` myself in the ode, then the result will contains 2 c's. The
> constant of integration `c` that sage uses, and my own `c` which I have in
> the ode itself. So how is a user to know which is which when they look at
> the result??
>
> reset()
> x,c= var('x c')
> y = function('y', x)
> desolve(diff(y,x)+c*y, y,ivar=x)
>
>
> which gives
>
> c*e^(-c*x)
>
> Is there a way to tell sage to use at least upper case letter for constant of
> integration?
>
> This is how Mathematica does it:
>
> In[67]:= DSolve[y'[x]+c*y[x]==0,y[x],x]
> Out[67]= {{y[x]->E^(-c x) C[1]}}
>
>
> You can see it is easy to see which is the constant of integration in the
> result. If there are
> more than one constant of integrations, they become C[1], C[2], etc....
>
> same with Maple
>
> dsolve(diff(y(x),x)+c*y(x)=0);
> y(x) = _C1 exp(-c x)
>
>
> see, it uses _C1
>
> How can one make sage change this behavior so it is easier to read the
> results? lower case
> letters for constant of integrations is not really a good way to do this.
>
> thanks,
>
>
>
>
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