pdsolve_pde

Solves partial differential equations (PDEs) using symbolic computation. Input the expression key and function name to generate a LaTeX-formatted solution for the specified PDE.

Instructions

Solves a partial differential equation using SymPy's pdsolve function.

Args:
    expr_key: The key of the expression (previously introduced) containing the PDE.
             If the expression is not an equation (Eq), it will be interpreted as
             PDE = 0.
    func_name: The name of the function (previously introduced) to solve for.
               This should be a function of multiple variables.

Example:
    # First introduce variables and a function
    intro("x", [Assumption.REAL], [])
    intro("y", [Assumption.REAL], [])
    introduce_function("f")

    # Create a PDE: 1 + 2*(ux/u) + 3*(uy/u) = 0
    expr_key = introduce_expression(
        "Eq(1 + 2*Derivative(f(x, y), x)/f(x, y) + 3*Derivative(f(x, y), y)/f(x, y), 0)"
    )

    # Solve the PDE
    result = pdsolve_pde(expr_key, "f")
    # Returns solution with exponential terms and arbitrary function

Returns:
    A LaTeX string representing the solution. Returns an error message string if issues occur.

Input Schema

Name	Required	Description	Default
`expr_key`	Yes
`func_name`	Yes
`hint`	No

Input Schema (JSON Schema)

{
  "$defs": {
    "PDEHint": {
      "enum": [
        "1st_linear_constant_coeff_homogeneous",
        "1st_linear_constant_coeff",
        "1st_linear_constant_coeff_Integral",
        "1st_linear_variable_coeff"
      ],
      "title": "PDEHint",
      "type": "string"
    }
  },
  "properties": {
    "expr_key": {
      "title": "Expr Key",
      "type": "string"
    },
    "func_name": {
      "title": "Func Name",
      "type": "string"
    },
    "hint": {
      "anyOf": [
        {
          "$ref": "#/$defs/PDEHint"
        },
        {
          "type": "null"
        }
      ],
      "default": null
    }
  },
  "required": [
    "expr_key",
    "func_name"
  ],
  "title": "pdsolve_pdeArguments",
  "type": "object"
}

Symbolic Algebra MCP Server

pdsolve_pde

Instructions

Input Schema

Input Schema (JSON Schema)

Other Tools from Symbolic Algebra MCP Server

Related Tools

MCP directory API