Add `modelingtoolkitize` function

[YingboMa]

using ModelingToolkit, DiffEqBase, OrdinaryDiffEq

function lotka(du,u,p,t)
  x = u[1]
  y = u[2]
  du[1] = p[1]*x - p[2]*x*y
  du[2] = -p[3]*y + p[4]*x*y
end

prob = ODEProblem(lotka,[1.0,1.0],(0.0,1.0),[1.5,1.0,3.0,1.0])

function modelingtoolkitize(prob::DiffEqBase.DEProblem)
    t, = @parameters t; vars = [Variable(Symbol(:x, i))(t) for i in eachindex(prob.u0)]; params = [Variable(Symbol(:α, i); known = true)() for i in eachindex(prob.p)];
    D, = @derivatives D'~t

    rhs = [D(var) for var in vars]

    if DiffEqBase.isinplace(prob)
        lhs = similar(vars, Any)
        prob.f(lhs, vars, params, t)
    else
        lhs = prob.f(vars, params, t)
    end

    eqs = vcat([rhs[i] ~ lhs[i] for i in eachindex(prob.u0)]...)
    de = ODESystem(eqs)

    f = ODEFunction(de, vars, params)

    prob = remake(prob, f=f)
end

solve(modelingtoolkitize(prob), Tsit5())

[ChrisRackauckas]

I think it should kick out the ODESystem instead of the problem, so that way the user can make use of the generated system (and for example get the symbolic Jacobian)