Add a flag to turn off dummy derivative

Author: ChrisRackauckas

src/systems/systemstructure.jl

@@ -616,6 +616,7 @@ end
 
 function _structural_simplify!(state::TearingState, io; simplify = false,
         check_consistency = true, fully_determined = true, warn_initialize_determined = false,
+        dummy_derivative = true,
         kwargs...)
     check_consistency &= fully_determined
     has_io = io !== nothing
@@ -628,7 +629,7 @@ function _structural_simplify!(state::TearingState, io; simplify = false,
     if check_consistency
         ModelingToolkit.check_consistency(state, orig_inputs)
     end
-    if fully_determined
+    if fully_determined && dummy_derivative
         sys = ModelingToolkit.dummy_derivative(sys, state; simplify, mm, check_consistency)
     else
         sys = ModelingToolkit.tearing(sys, state; simplify, mm, check_consistency)