Update checks and docs

Author: YingboMa

docs/src/mtkitize_tutorials/modelingtoolkitize_index_reduction.md

@@ -29,8 +29,8 @@ p = [9.8, 1]
 tspan = (0, 10.0)
 pendulum_prob = ODEProblem(pendulum_fun!, u0, tspan, p)
 traced_sys = modelingtoolkitize(pendulum_prob)
-pendulum_sys = structural_simplify(traced_sys)
-prob = ODAEProblem(pendulum_sys, Pair[], tspan)
+pendulum_sys = structural_simplify(dae_index_lowering(traced_sys))
+prob = ODAEProblem(pendulum_sys, [], tspan)
 sol = solve(prob, Tsit5(),abstol=1e-8,reltol=1e-8)
 plot(sol, vars=states(traced_sys))
 ```

src/systems/diffeqs/abstractodesystem.jl

@@ -106,8 +106,8 @@ function generate_function(
     eqs = [eq for eq in equations(sys) if !isdifferenceeq(eq)]
     if !implicit_dae
         check_operator_variables(eqs, Differential)
+        check_lhs(eqs, Differential, Set(dvs))
     end
-    check_lhs(eqs, Differential, Set(dvs))
     # substitute x(t) by just x
     rhss = implicit_dae ? [_iszero(eq.lhs) ? eq.rhs : eq.rhs - eq.lhs for eq in eqs] :
                           [eq.rhs for eq in eqs]