How to define the DAE using du[] style

here is another windkessel model in the simulation, from “The differential-algebraic Windkessel model with power as input” by Henry Pigot.
I don’t know to define the DAE using Julia common package like DifferentialEquations.jl, as the bellow style.
function lorenz(u, p, t)
dx = 10.0 * (u[2] - u[1])
dy = u[1] * (28.0 - u[3]) - u[2]
dz = u[1] * u[2] - (8 / 3) * u[3]
[dx, dy, dz]
Finally, I want to use the ODEProblem() to solve it and do some parameter estimations.
thanks for any suggestions.

You can either define a mass matrix (with zeros on the diagonal for algebraic equations).

Or, you could provide a vector of Booleans for denoting which variables are differential/algebraic.

See the examples here: Differential Algebraic Equations · DifferentialEquations.jl

What have you tried?

Did you follow the tutorial and try writing one?

would you please give any suggestions?

I don’t think it’s ethical for us to do your homework for you. But the advice I would have is to just use ModelingToolkit.jl for defining and solving the DAE system.

There’s some other real-world advantages you’d get from that as well, since it would ensure the DAE is lowered to index 1 form.

thanks. I am learning Julia following the examples, not mean my homework.
this is open discourse, anyone who once solved the samilary question can give suggestion or just pass by.
I am always grateful for the helps I got here.