desolve mixes user parameters and integration constants

[zimmermann6]

Consider

sage: var('t')
sage: x=function('x',t)
sage: var('c')
sage: desolve(diff(x,t)+2*x==t^2-2*t+c,x,ivar=t).expand()
c*e^(-2*t) + 1/2*t^2 + 1/2*c - 3/2*t + 3/4

Here the first occurrence of c is an integration constant,
whereas the second one is the parameter in the ODE:

sage: var('d')
sage: desolve(diff(x,t)+2*x==t^2-2*t+d,x,ivar=t).expand()
c*e^(-2*t) + 1/2*t^2 + 1/2*d - 3/2*t + 3/4

In case the ODE contains c, desolve should choose another
name for the integration constant.

CC: @robert-marik @kcrisman

Component: calculus

Author: Paul Zimmermann

Reviewer: Ralf Stephan

Issue created by migration from https://trac.sagemath.org/ticket/9421

[robert-marik]

comment:1

This is a part of more general problem which has been reported in #6882.

[zimmermann6]

Attachment: trac_9421.patch.gz

[zimmermann6]

Author: Paul Zimmermann

[zimmermann6]

comment:4

waiting for the general problem to be solved, the attached patch prints a warning if the given equation contains the variable c.

Paul

[rwst]

comment:6

I will OK this if you have a look at #8734 in turn, please 8) See also #16007