Starting collaboration through first e-mail. Can it work?
Let's elaborate on my comment in this answer. Here are the issues:
- There are just statements in your draft, no actual question.
- The tone of the mail is a bit informal for the case you don't know Prof. Y (at least in my opinion). Leaving out the "Greetings" will make it better.
Here's my proposal for the mail:
Subject: Request for collaboration -- Problem A and Problem B
Dear Prof. Y,
I have learned about you from Prof. X during my works with him.
I have gone through your recent papers: [this] and [this]. Recently, I have worked with Method1 and Method2 which could suitably address your problem. Would you be interested to (Removed: collaborate on [thing] with me?) talk with me about the topic in a phone call or meeting? It would be a pleasure to work with you on this topic.
My recent works can be found in [this profile link].
Looking forward to hearing from you.
Sincerely,
me
-- [my signature]
Of course it can work, it is done all the time. Right now we got several projects running with other groups all around the world, some of them started with a mail basically saying "hey, you are doing nice work, we got an idea and would need your help, are you interested?".
For your situation it depends on what you want from this collaboration. Do you want them to do a part of that project because they can do it (better)? Or do you want to go there and learn how to do it yourself, which is more like an internship. Or do you have a solution to a problem they are having, which is in my opinion not a common reason to start a cooperation.
I agree with @ian_itor that your mail basically doesn't say anything about what you want from that Prof. Y. And especially this part is kind of strange:
I am good in Method1 and Method2 which could suitably address your problem.
Is beeing good in that method something special? Couldn't they do it alone/find someone else? Do they really need YOU? Did they explicitly stated that they have this problem? And do you need them?