be busy doing sth 与be busily doing的区别

be busy doing sth.正在忙着做什么
没有be busily doing这种说法，可以说be doing sth. busily=be busy doing sth.

be busy doing 是一个固定搭配
be busily doing 没有这样固定的说法,但是也没有错,我们可以这样理解,我举个例子:
She is busily doing homework.
此时busily是作为副词来修饰do 的,而do 之所以加ing是因为这个句子的时态是现在进行时,be动词后加ing 形式

I do not know how to explain in Chinese.
There is no significant difference between them.
Be busily doing 强调繁忙的做某事
Be busy doing sth 强调很忙的状态
I am busily crunching numbers now.
I am busy crunching numbers now.

be busy doing sth.=be doing sth. busily
都是“忙于做某事”的意思
busy 做形容词，修饰动名词doing
busily做副词，修饰动词do(doing是现在分词）