For fun:

If you want to ``see'' your solutions, add the following statements to the end of your program

  rho.printr("rho");
  phi.printr("phi");
  phianal.printr("phianal");

This will make three files that you can plot: ``rho,'' ``phi'' and ``phianal.'' The three columns in each file are (1) distance from the origin, and (2) the real and (3) imaginary parts of either rho, phi or phianal.