I am trying to solve the spherical harmonics PDE in Mathemtica. My code is:
pde = 1/Sin[\[Theta]]^2 D[f[\[Theta], \[Phi]], {\[Phi], 2}] +
Cot[\[Theta]] D[f[\[Theta], \[Phi]], \[Theta]] +
D[f[\[Theta], \[Phi]], {\[Theta], 2}] + c f[\[Theta], \[Phi]] == 0
DSolve[ pde, f[\[Theta], \[Phi]], {\[Theta], \[Phi]}]
DSolve seems to be unable to solve this PDE. Am I making a mistake here somewhere?
c*f
which I do not know where it came from. different from SphericalHarmonicDifferentialEquation $\endgroup$