fain

[feyn] /feɪn/
adverb
1.
gladly; willingly:
He fain would accept.
adjective
2.
content; willing:
They were fain to go.
3.
Archaic. constrained; obliged:
He was fain to obey his Lord.
4.
Archaic. glad; pleased.
5.
Archaic. desirous; eager.
Origin
before 900; Middle English; Old English fæg(e)n; cognate with Old Norse feginn happy; akin to fair1
Can be confused
fain, faint, feign, feint.
British Dictionary definitions for fain

fain

/feɪn/
adverb
1.
(usually with would) (archaic) willingly; gladly: she would fain be dead
adjective
2.
(obsolete)
  1. willing or eager
  2. compelled
Word Origin
Old English fægen; related to Old Norse fegiun happy, Old High German gifehan to be glad, Gothic fahehs joy; see fawn²
Word Origin and History for fain
adj.

Old English fægen, fagen "glad, cheerful, happy, joyful, rejoicing," from a common Germanic root (cf. Old Saxon fagan, Old Norse feginn "glad," Old High German faginon, Gothic faginon "to rejoice"), perhaps from PIE *pek- "to make pretty." As an adverb, from c.1200.