我来补充一下楼上二位的话。
Just adding to what Daniel and Amy was saying,
“轻易地” in some context implied that the object of interest should have been a difficult / challenging feat (yet it was accomplished 轻易地)。
here are some examples. In these sentences, if you are using 轻松地 instead-- although we can understand what you are trying to say, it sounds a lot less natural.
✤ 你怎么能这么轻易地就把我忘了呢?
How could you have forgotten about me already?!
(imply: I'm a very important person to you, forgetting me would be difficult; it has hurt my feelings a great deal)
✤那道题我怎么都不会做,可是Aki没花多长时间就轻易地做出来了。
That problem was so difficult that I couldn't get it done in forever, but it only took Aki a few minutes to easily solve it.
(imply: It's hard for me, the speaker, to reconcile to)
✤身为一个国家的国王,他怎么能轻易地投降呢。
as a king of a kingdom, how can he easily surrender.
(imply: that would be cowardly and unethical.)
✤这东西很危险,千万不要轻易靠近。(地was emitted)
This thing is dangerous, do not approach rashly.
(rashly: in this sentence you can also replace 轻易 with 贸然)
in this case, using 轻松 would be absolutely wrong.
In all my previous examples, the overtone/ connotations sounded somewhat negative, with degrees ranging from trivial stuff to serious matter. In contrary, 轻松 in many cases simply means the level of difficulty was low.
Then, in what cases 轻松 would be more appropriate?
You can refer back to Amy's answer ("take it easy")
Of course, there are many cases in which they are completely interchangeable. :D
Good luck studying!