Unexpected result from DSolve?

[mrtclskn95 (Mert Caliskan)]

Hello,
How can i solve this problem? I have tried to solve with mathematica but it does not answer correctly
Could you kindly help me?

[gianlucagorni]

I think that it is an operator square, not a numeric square:

op[expr_, r_] := D[expr, r, r] + 1/r D[expr, r];
DSolve[op[op[f[r], r], r] == 0, f, r]

[mrtclskn95 (Mert Caliskan)]

Thank you very much it is correct.
Also could you help me on this?

[gianlucagorni]

Just use the modified operator D[expr, r, r] + 1/r D[expr, r] - 4/r^2 expr.