Better show methods which include AD info for stiff solvers

[ArnoStrouwen]

The following two look the same:

julia> Rodas5P()
Rodas5P(; linsolve = nothing, precs = DEFAULT_PRECS,)
julia> sol.alg # comming from the default alg selector
Rodas5P(; linsolve = nothing, precs = DEFAULT_PRECS,)

But are not:

julia> typeof(Rodas5P())
Rodas5P{0, true, Nothing, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}

julia> typeof(sol.alg)
Rodas5P{1, false, Nothing, typeof(OrdinaryDiffEq.DEFAULT_PRECS), Val{:forward}, true, nothing}

It is super easy for the user to copy and paste the result from the show method and end up with a different solver. The constructor with the autodiff keywords and so on should be printed instead.

[ChrisRackauckas]

Interesting, I didn't know we had a show method on that.