Partial Differential Equations

PDEs can be also solved with the sympy module and the pdsolve function.

Here is how this can be done, step by step to solve the PDE 1 + (2(ux/u)) + (3(uy/u)):

1. Import sympy

    from sympy.solvers.pde import pdsolve
    from sympy import Function, Eq
   

2. Create symbols

   We need to tell sympy that the letters x and y represents a symbol whilst f is a function..

    from sympy.abc import x, y
    f = Function('f')
   

3. Calculate derivatives and define equation

    u = f(x, y)
    ux = u.diff(x)
    uy = u.diff(y)
   
    eq = Eq(1 + (2*(ux/u)) + (3*(uy/u)), 0)
   

4. Solve the PDE.

    pdsolve(eq)