This is NOT an exhaustive analysis of New Testament occurrances of the word that equates to peitho nor of extrabiblical use; nonetheless, it provides insight.  

A few notes to help with reading this table:

• The first three bullet items show the same lexicon website page, with the third containing the precise same Greek word as Hebrews 13:17 (πείθεσθε); however, Hebrews 13:17 is not listed.
• The next two bullet items show the single usage of πείθεσθε extrabibllically on this particular lexicon
• The final bullet item is Hebrews 13:17 containing πείθεσθε

 

All images link to the lexicon website.  

• Lexicon (link to peitho definition top of page)
• Lexicon (link to peitho definition imprecise Greek match mid page)
• Lexicon (link to peitho definition precise Greek match lower in page EXACT GREEK MATCH)
• Lexicon (link to peitho in English writing: Aristophanes, Thesmophoriazusae, 593)
• Lexicon (link to peitho in Greek writing: Aristophanes, Thesmophoriazusae, 593)
• Lexicon (link to peitho in Hebrews 13:17)