mutually vs sympathetically

mutually

adv
  • in a shared manner; equally; affecting all parties the same way 

  • in the same way, each to the other; reciprocally 

sympathetically

adv
  • In a manner which demonstrates a sharing in the feelings of others; compassionately. 

  • Owing to or showing evidence of sympathy, or affinity; happening through or demonstrating correspondences, whether occult or physiological. 

How often have the words mutually and sympathetically occurred in a corpus of books? (source: Google Ngram Viewer )