Laplace operator in spherical coordinates (with angular symmetry)

[Gert Van den Eynde]

Hi,

I was trying to solve the laplace equation in spherical coordinates with angular symmetry:

from sympy.interactive import printing
printing.init_printing()
import sympy as sym
r = sym.symbols('r')
f= sym.Function('f')

eq = sym.Eq(sym.Derivative(r**2*sym.Derivative(f(r),r),r) + r**2*f(r) , 0)
display(eq)
sym.classify_ode(eq,f(r))
sym.dsolve(eq,f(r))


returns

[...]

NotImplementedError: solve: Cannot solve r**2*f(r) + r**2*Derivative(f(r), r, r) + 2*r*Derivative(f(r), r)

As far as I understand Sympy's classify_ode and dsolve do not recognize this equation. Or am I missing something?

Is this expected behaviour?

Best regards,
Gert

[Aaron Meurer]

I haven't kept up to date with the dsolve work that was done this
summer, but from as far as I know, there are no solvers implemented to
handle this one. Do you know what a good method to solve it would be,
which can be implemented?

Aaron Meurer

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