Support null u0 with callbacks for all solvers

When `u0 === nothing`, convert u to an empty Float64 array to allow
initialization to proceed. This enables problems with no state variables
but with callbacks to be solved with any solver.

Changes:
1. OrdinaryDiffEqCore/src/solve.jl: Convert null u0 to Float64[]
2. OrdinaryDiffEqDifferentiation/src/derivative_wrappers.jl: Skip Jacobian
   computation for empty state vectors

This fixes the issue where MTK systems that simplify to having no differential
equations (resulting in `u0 === nothing`) but have `SymbolicDiscreteCallback`
could not trigger callbacks.

Tested with explicit (FunctionMap, Tsit5, Euler, RK4) and implicit
(Rosenbrock23, Rodas5P, TRBDF2, KenCarp4, ImplicitEuler, QNDF, FBDF) solvers.

References: SciML/ModelingToolkit.jl#4078

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude Opus 4.5 <[email protected]>

Author: ChrisRackauckas

lib/OrdinaryDiffEqCore/src/solve.jl

@@ -212,6 +212,12 @@ function SciMLBase.__init(
         u = recursivecopy(prob.u0)
     end
 
+    # Handle null u0 (e.g., MTK systems with only callbacks and no state variables)
+    # Convert to empty Float64 array to allow initialization to proceed
+    if u === nothing
+        u = Float64[]
+    end
+
     if _alg isa DAEAlgorithm
         if !isnothing(aliases.alias_du0) && aliases.alias_du0
             du = prob.du0

lib/OrdinaryDiffEqDifferentiation/src/derivative_wrappers.jl

@@ -186,6 +186,11 @@ end
 function jacobian!(J::AbstractMatrix{<:Number}, f::F, x::AbstractArray{<:Number},
         fx::AbstractArray{<:Number}, integrator::SciMLBase.DEIntegrator,
         jac_config) where F
+    # Handle empty state vector - nothing to compute
+    if isempty(x)
+        return nothing
+    end
+
     alg = unwrap_alg(integrator, true)
 
     dense = ADTypes.dense_ad(alg_autodiff(alg))