add an example for parsing Julia expressions into ModelingToolkit solves

With known limitations documented in JuliaSymbolics/Symbolics.jl#808

Author: ChrisRackauckas

docs/pages.jl

@@ -9,7 +9,8 @@ pages = [
                        "tutorials/parameter_identifiability.md"],
     "Examples" => Any["Basic Examples" => Any["examples/higher_order.md",
                                               "examples/spring_mass.md",
-                                              "examples/modelingtoolkitize_index_reduction.md"],
+                                              "examples/modelingtoolkitize_index_reduction.md",
+                                              "examples/parsing.md"],
                       "Advanced Examples" => Any["examples/tearing_parallelism.md",
                                                  "examples/sparse_jacobians.md",
                                                  "examples/perturbation.md"]],

docs/src/examples/parsing.md

@@ -0,0 +1,32 @@
+# Parsing Expressions into Solvable Systems
+
+Many times when creating DSLs or creating ModelingToolkit extensions to read new file formats,
+it can become imperative to parse expressions. In many cases, it can be easy to use `Base.parse`
+to take things to standard Julia expressions, but how can you take a `Base.Expr` and generate
+symbolic forms from that? For example, say we had the following system we wanted to solve:
+
+```@example parsing
+ex = [:(y ~ x)
+      :(y ~ -2x + 3 / z)
+      :(z ~ 2)]
+```
+
+We can use the function `parse_expr_to_symbolic` from Symbolics.jl to generate the symbolic
+form of the expression:
+
+```@example parsing 
+Symbolics
+eqs = parse_expr_to_symbolic.(ex, (Main,))
+```
+
+From there, we can use ModelingToolkit to transform the symbolic equations into a numerical
+nonlinear solve:
+
+```@example parsing
+using ModelingToolkit, NonlinearSolve
+vars = union(ModelingToolkit.vars.(eqs)...)
+@named ns = NonlinearSystem(eqs, vars, [])
+
+prob = NonlinearProblem(ns,[1.0,1.0,1.0])
+sol = solve(prob,NewtonRaphson())
+```