Idea Proposal: Adding Lagrange & Charpit Methods for First-Order PDEs in SymPy

[Monu kumar]

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