Update return code documentation to reflect enum implementation (fixes #734)

- Update retcode documentation to explain they are now enum values, not symbols
- Add proper usage example with SciMLBase.successful_retcode(sol)
- Add warning about deprecated sol.retcode == :Success pattern
- Fix incorrect usage in FAQ (was sol.retcode, should be just sol)
- Add link to SciMLBase ReturnCode documentation for complete reference

This addresses the issue where the documentation was outdated and still
described return codes as symbols instead of the current enum implementation.

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

docs/src/basics/faq.md

@@ -32,7 +32,7 @@ the solution quickly diverges to infinity! This means, double-check your paramet
 are indexed correctly!
 
 **Note: if you see these warnings during a parameter estimation process, this is
-likely the underlying problem. Simply check `SciMLBase.successful_retcode(sol.retcode)` and throw
+likely the underlying problem. Simply check `SciMLBase.successful_retcode(sol)` and throw
 an `Inf` cost. Most optimizers will then reject steps in those parameter regimes!**
 
 There are a few other things to check as well. Often, the stability of

docs/src/basics/solution.md

@@ -181,23 +181,38 @@ SciMLBase.DEStats
 
 ## [Return Codes (RetCodes)](@id retcodes)
 
-The solution types have a `retcode` field which returns a symbol signifying the
-error state of the solution. The retcodes are as follows:
+The solution types have a `retcode` field which returns an enum value signifying the
+error state of the solution. Return codes are now implemented as an enum using EnumX.jl
+rather than symbols.
 
-  - `:Default`: The solver did not set retcodes.
-  - `:Success`: The integration completed without erroring or the steady state solver
+To check if a solution was successful, use:
+```julia
+SciMLBase.successful_retcode(sol)
+```
+
+!!! warning
+    Previous iterations of the interface suggested using `sol.retcode == :Success`, 
+    however, that is now not advised. Use `SciMLBase.successful_retcode(sol)` instead.
+
+The return codes include:
+
+  - `Default`: The solver did not set retcodes.
+  - `Success`: The integration completed without erroring or the steady state solver
     from `SteadyStateDiffEq` found the steady state.
-  - `:Terminated`: The integration is terminated with `terminate!(integrator)`.
+  - `Terminated`: The integration is terminated with `terminate!(integrator)`.
     Note that this may occur by using `TerminateSteadyState` from the callback
     library `DiffEqCallbacks`.
-  - `:MaxIters`: The integration exited early because it reached its maximum number
+  - `MaxIters`: The integration exited early because it reached its maximum number
     of iterations.
-  - `:DtLessThanMin`: The timestep method chose a stepsize which is smaller than the
+  - `DtLessThanMin`: The timestep method chose a stepsize which is smaller than the
     allowed minimum timestep, and exited early.
-  - `:Unstable`: The solver detected that the solution was unstable and exited early.
-  - `:InitialFailure`: The DAE solver could not find consistent initial conditions.
-  - `:ConvergenceFailure`: The internal implicit solvers failed to converge.
-  - `:Failure`: General uncategorized failures or errors.
+  - `Unstable`: The solver detected that the solution was unstable and exited early.
+  - `InitialFailure`: The DAE solver could not find consistent initial conditions.
+  - `ConvergenceFailure`: The internal implicit solvers failed to converge.
+  - `Failure`: General uncategorized failures or errors.
+
+For a complete list of return codes and their properties, see the 
+[SciMLBase ReturnCode documentation](https://docs.sciml.ai/SciMLBase/stable/interfaces/Solutions/#retcodes).
 
 ## Problem-Specific Features