cheer up!; chin up!; keep your spirits up!
A warm, encouraging phrase used to cheer someone up who seems down or tired. Often said to a friend or family member.
Cheer up, tomorrow will surely be a better day.
Don't make that face; keep your chin up.
Means 'do your best' or 'hang in there,' focusing on effort. 元気出して is more about emotional encouragement and lifting someone's mood.
From 元気 (げんき, 'energy, spirit') + 出して (だして, the te-form of 出す, 'to put out'), literally 'put out your energy/spirit.'