Error with supposedly normal DE problem

[kcrisman]

See this ask.sagemath.org question.

var('a b n k t')
c = function('c',t)
de = diff(c,t) - a + (b*c)*((c**n)/((k**n)+(c**n))) == 0
des = desolve(de,[c,t],[0,0])

yields an error about c(t) not being a proper Python identifier. Various other combinations yield similar ECL errors, and at least sometimes one can get segmentation faults after inserting print statements.

CC: @sagetrac-schymans

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/14092

[kcrisman]

comment:1

Simpler example that seems to behave analogously.

de = diff(c,t) - a + c^n == 0

Note that making n a specific integer gives questions about the sign of a and assume(a>0) fixes things.

Are there maybe just too many variables?

[sagetrac-schymans]

comment:2

I don't think it is about the number of variables, but about maxima not being able to provide an explicit solution. Here is the example computed directly in maxima:

maxima("de: 'diff(c(t),t) - a + c(t)^n")
maxima("atvalue (c(t), t = 0, 0);")
maxima("ode2(de,c(t),t);")

gives:

-'integrate(1/(c(t)^  n-a),c(t))=t+%c

Note that the integral containing c(t)ⁿ could not be solved.
Replacing n by an integer and defining c as positive:

maxima("de: 'diff(c(t),t) - a + c(t)^2")
maxima("atvalue (c(t), t = 0, 0);")
maxima("assume(a>0);")
maxima("ode2(de,c(t),t);")

gives:

-log(-(sqrt(a)-c(t))/(c(t)+sqrt(a)))/(2*sqrt(a))=t+%c

Is it possible that the 'integrate in the solution creates a problem?

[rwst]

comment:8

With #22024 we get:

sage: solve(de,t,algorithm='sympy')
ConditionSet(t, Eq(-a*(k**n + c(t)**n) + b*c(t)*c(t)**n + (k**n + c(t)**n)*Derivative(c(t), t), 0), Complexes(S.Reals x S.Reals, False)) \ ConditionSet(t, Eq(k**n + c(t)**n, 0), Complexes(S.Reals x S.Reals, False))