<< Miscellaneous`PhysicalConstants`

VacuumPermittivity

<< Calculus`VectorAnalysis`

SetCoordinates[Cylindrical[r, fi, z]];

Havektor = {0, 0, Hz[r, t]};
Evektor = {0, Efi[r, t], 0};
rotHa = Curl[Havektor];
rotE = Curl[Evektor];
rce1 = 
      rotHa[[2]] == γ*Efi[r, t]
rce2 = rotE[[3]] == D[μ*Hz[r, t], t]

dosEfi = Solve[rce1, Efi[r, t]][[1]]

Union[dosEfi, D[dosEfi, r]]

trochuupraveno = 
      rce2 /. Union[dosEfi, D[dosEfi, r]] // Simplify

dale = 
      trochuupraveno /. 
        a_ == b_ -> 
          Simplify[(a - b)*r*γ] == 0

rcevcase = Simplify[dale]

rcefazory=rcevcase/.{Derivative[1, 0][Hz][r, t]->Hzf'[r],Derivative[2, 0][Hz][r, t]->Hzf''[r],Derivative[0, 1][Hz][r, t]->I*ω*Hzf[r]}

DSolve[rcefazory, Hzf[r], r] // 
        Simplify[#, {γ > 0, μ > 0, ω > 0}] & // 
      N

BesselI