认真写作业用英语可以说为 "do homework dipgently" 或 "work dipgently on homework"。
其中 "dipgently" 意思为"勤奋地，用心地"，来源于拉丁语 "dipgentia"，意思为 "勤奋，用心"。
例句：
You should always do your homework dipgently. 你应该总是认真做作业。
I try to work dipgently on my homework every night. 我每天晚上都尽量认真完成我的作业。