Update DAE tutorial with initialization information and BrownFullBasicInit examples

[ChrisRackauckas-Claude]

Summary

This PR updates the DAE tutorial to include comprehensive information about DAE initialization, particularly focusing on the use of with the IDA solver.

Changes Made

Added DAE Initialization Section

• Explains why DAEs require consistent initial conditions
• Shows how to use the parameter with IDA
• Demonstrates both and

Added Practical Example

• Shows what happens with inconsistent initial conditions
• Demonstrates how automatically corrects algebraic variables
• Includes output showing the correction process

Documentation Improvements

• Clarified that is needed for initialization algorithms
• Added link to the comprehensive DAE initialization documentation
• Improved explanation of constraint satisfaction

Motivation

With the recent changes in Sundials.jl v5.0 where DAE initialization is no longer automatic by default, it's crucial that the tutorial explicitly shows users how to handle initialization. This update ensures new users understand:

1. Why initialization matters for DAEs
2. How to use initialization algorithms
3. What happens when initial conditions are inconsistent
4. How the solver fixes inconsistencies

Example Code

The tutorial now includes:

• Basic usage:
• Verification:
• Handling inconsistent conditions with automatic correction

This makes the tutorial more complete and helps users avoid common pitfalls when solving DAE problems.