Solving systems with sensitivity states as Differentials

[ArnoStrouwen]

using ModelingToolkit
using OrdinaryDiffEq
@parameters t
@variables u(t)
@derivatives D'~t
@parameters k 
@derivatives Dk'~k

eqs = [D(u)     ~ -k*u,
       D(Dk(u)) ~ -u-k*(Dk(u))]
sys = ODESystem(eqs, t, [u,Dk(u)], [k])
#ODESystem(eqs) #does not work
p_map = [k => 1.0]
u0_map = [u => 1.0
         Dk(u) => 0.0]
prob = ODEProblem(sys,u0_map,(0.0,1.0),p_map)
solve(prob,Tsit5()) # does not work

[ChrisRackauckas]

D(Dk(u)) lowers to uˍt(t): @YingboMa do we still need to be doing that?

[ChrisRackauckas]

#398 is connected. I think if we can just use those variables then we're fine, and I think Pantelides does something like it so I'm confused why it works.