Put utilities for solve in SciMLBase

[jClugstor]

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

This time for real and without Static

[ChrisRackauckas]

Why is this needed in SciMLBase?

[jClugstor]

anyeltypedual is used in promote_u0, which is used by get_concrete_problem for NonlinearProblem and also differential equations. So it's needed for both. So this either needs to be in SciMLBase, or it needs to be in both DiffEqBase and NonlinearSolveBase.

[ChrisRackauckas]

why would nonlinearproblem need it? It should use implicit diff, and it requires p as an array for that just like linearproblem?

[jClugstor]

Well promote_u0 is also used for a few other things, like Tracker, ReverseDiff, Measurements, and Montecarlo measurements. So we still need to use promote_u0 for NonlinearProblems in those cases.

Also,
Current behavior:

using NonlinearSolve
using ForwardDiff

f(u, p) = u .* u .- p
u0 = [1.0, 1.0]
p = ForwardDiff.Dual(2.0, 1.0)
prob = NonlinearProblem(f, u0, p)
sol = solve(prob)

in the solve call u0 does get promoted to Dual through promote_u0 and the problem passed to solve_call actually does have a dual u0. Of course it ends up being stripped in the overloads, but I didn't really want to mess with the current behavior.

So we could put anyeltypedual back in to DiffEqBase, but we would also need to put promote_u0 back in that case because it uses anyeltypedual. We would just need each FooBase package to define it's own implementation or variation of promote_u0 in that case.