fix: fix initialization with defaults dependent on indepvar

[AayushSabharwal]

Close #2799

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[hersle]

I think the only problem is that t should not be substituted for DDEs. Same as in #2877.

[AayushSabharwal]

Thank you! I never would've found that

[AayushSabharwal]

Is there any way to check if an ODESystem represents a DDE?

[hersle]

From what I understand in test/dde.jl, it is not possible to tell at the system level; only the problem level (since DDE systems are ODESystems, but DDE problems are DDEProblems).

Maybe process_DEProblem(constructor, ...; symbolic_u0, ...) could check if constructor isa DDEFunction || constructor isa SDDEFunction, and if so pass t0 = nothing to get_u0*()? Alternatively, it looks to me like symbolic_u0 = true is passed if (and only if) the system/problem is a (S)DDE, so maybe it could check if symbolic_u0 instead?

[hersle]

Nice. This looks good now?