Partial differential equation (Diffusion equation in spherical coordinates)

Questions
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1

Can I please get a help with partial differential equation in mathematica? I tried but got no where. It’s a diffusion in a spherical coordinate. Here is the how I tried to solve it and IO added the attachment.

rin = 0.003; rout = 0.00345; cmeq = 0.0245;

sol1 = DSolve[{D[cm[t, r], t] == (1/r)^2* D[difcoef*r^2*D[cm (t, r), r], r], cm (0, r) == cmo, 
cm (t, rout) == cmeq, D[cm (t, rin), r] == 0}, cm (t, r), {t, r}]
2

I don’t get anything from DSolve, but NDSolve gives a solution with proper syntax:

With[{difcoefr = 1, cmo = 1, rin = 1, rout = 2, cmeq = 1}, 
 NDSolve[{D[cm[t, r], t] == (1/r)^2*D[difcoefr^2 D[cm[t, r], r], r], 
   cm[0, r] == cmo, 
   cm[t, rout] == cmeq, (D[cm[t, r], r] /. r -> rin) == 0}, 
  cm, {t, 0, 1}, {r, rin, rout}]]