Hello Sympy Community,

I hope you’re doing well.

Myself Monu kumar, and I’ve been exploring SymPy’s current support for 
partial differential equations as part of my preparation for open-source 
contributions and GSoC. While studying sympy.solvers.pde, I noticed that 
although pdsolve supports some first-order PDEs, there is no explicit 
implementation of classical methods like *Lagrange’s auxiliary equations* 
and *Charpit’s method* for first-order PDEs.

I wanted to ask whether adding structured support for these methods would 
be a valuable contribution to SymPy.

My initial idea is to:

   - 
   
   Implement *Lagrange’s method* for linear first-order PDEs of the form
   P(x,y,z)p + Q(x,y,z)q = R(x,y,z)
   - 
   
   Add a *restricted but extensible implementation of Charpit’s method* for 
   nonlinear first-order PDEs
   - 
   
   Keep the implementation modular under sympy/solvers/pde, with proper 
   tests and documentation
   - 
   
   Eventually integrate method selection into pdsolve once the core 
   functionality is stable
   
Before proceeding further, I would really appreciate your feedback on:

   1. 
   
   Whether this aligns with SymPy’s current PDE roadmap
   2. 
   
   Any design considerations or limitations I should be aware of
   3. 
   
   Whether you’d recommend starting with a smaller scoped subset
   
Thank you for your time and guidance. I’d be very happy to refine the idea 
based on your suggestions.

Best regards,

Monu kumar

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