The Collaborative International Dictionary of English v.0.48:

Dutiful \Du"ti*ful\, a.
   1. Performing, or ready to perform, the duties required by
      one who has the right to claim submission, obedience, or
      deference; submissive to natural or legal superiors;
      obedient, as to parents or superiors; as, a dutiful son or
      daughter; a dutiful ward or servant; a dutiful subject.
      [1913 Webster]

   2. Controlled by, proceeding from, a sense of duty;
      respectful; deferential; as, dutiful affection.

   Syn: Duteous; obedient; reverent; reverential; submissive;
        docile; respectful; compliant. -- Du"ti*ful*ly, adv.
        -- Du"ti*ful*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

dutifully
    adv 1: out of a sense of duty; in a dutiful manner; "he
           dutifully visited his mother every Sunday"