solving a Algebraic Differential Equation in Julia using modelingToolKit.JL

Question

I'm trying to solve a differential algebraic equation in Julia's modelingTookKit.JL, where the vector field has the form f(X) = 0.

I found an example of a DAE in the below link modelingToolkit.JL DAE](https://benchmarks.sciml.ai/html/DAE/ROBERDAE.html) with follwing code. However, when I replace say

D(y₁) ~ -k₁*y₁ + k₃*y₂*y₃

by

0 ~ -k₁*y₁ + k₃*y₂*y₃ - D(y₁)

I get an error. If someone knows of or could provide an example where the the equation of the vector field is only implicitly defined i.e. f(X) = 0, it would be much appreciated.

using OrdinaryDiffEq, DiffEqDevTools, Sundials, ModelingToolkit, ODEInterfaceDiffEq,
      Plots, DASSL, DASKR
using LinearAlgebra

@variables t y₁(t)=1.0 y₂(t)=0.0 y₃(t)=0.0
@parameters k₁=0.04 k₂=3e7 k₃=1e4
D = Differential(t)
eqs = [
  D(y₁) ~ -k₁*y₁ + k₃*y₂*y₃
  D(y₂) ~  k₁*y₁ - k₃*y₂*y₃ - k₂*y₂^2
  0 ~  y₁ + y₂ + y₃ - 1
]
@named sys = ODESystem(eqs)
simpsys = structural_simplify(sys)
mmprob = ODEProblem(sys,[],(0.0,1e5))
daeprob = DAEProblem(sys,[D(y₁)=>-0.04,
                              D(y₂)=>0.04,
                              D(y₃)=>0.0],[],(0.0,1e5))
odaeprob = ODAEProblem(simpsys,[],(0.0,1e5))

ref_sol = solve(daeprob,IDA(),abstol=1/10^14,reltol=1/10^14);
ode_ref_sol = solve(odaeprob,CVODE_BDF(),abstol=1/10^14,reltol=1/10^14);

probs = [mmprob,daeprob,odaeprob]
refs = [ref_sol,ref_sol,ode_ref_sol];

Answer 1

0 ~ -k₁*y₁ + k₃*y₂*y₃ - D(y₁)

is handled in this PR. This feature will be included in the next release of ModelingToolkit.jl. Also, note that you should use

simpsys = structural_simplify(sys)
mmprob = ODEProblem(simpsys,[],(0.0,1e5))

The structural_simplify function doesn't mutate the system.