My advice is to use whatever version your teacher approves, especially on a test he or she gives. But be aware that different than is not really incorrect.
For a good look at this topic, see this excellent WordPress article by Stan Carey called different-from-different-than-different-to.
See also the same question Which is correct: "__ is different from__" or "__ is different than__" on sister site ELU.
Different from is apparently used more often than different than. However, different than is being used by more and more native speakers both in the USA and in the UK.
Some teachers and grammarians insist that different from is "correct" and that different than is "incorrect." This is called 'prescriptive grammar', insisting that people talk or write in a certain way, and that labels one expression as "correct" and another expression as "wrong." Ironically, in many cases, these prescriptivists (colloquial: "grammar Nazis") are ignorant that the constructions they deplore have a long history of usage in English.
However, different than is now used so often by so many people, that the attempt to force people to use different from will never be successful. 'Descriptive grammar' describes how and what native speakers actually say and therfore what is grammatical according to actual usage.
I just watched Broadchurch, a British television series in which famed Shakespearen/Dr Who actor David Tennant says different than.
This shows that different than is used not only in the USA, but also in the UK.
Note that another common usage in British English (but not in American English) is different to.
The Oxford Dictionary Online (ODO) states:
Different from, different than, and different to: what are the distinctions between these three constructions, and is one more correct than the others? In practice, different from is both the most common structure and the most accepted. Different than is used chiefly in North America, although its use is increasing in British English. Because it can be followed by a clause, it is sometimes more concise than different from (compare "things are different than they were a year ago" with "things are different from the way they were a year ago"). Different to, although common in Britain, is disliked by traditionalists and sounds peculiar to American ears.
Three separate usage notes about these options are found at the thefreedictionary. Note that many dictionaries now have 'usage panels' that vote on whether a phrase or usage is "acceptable" or not. This is just prescriptive grammar by vote. However, if the voting of the usage panel is close, than we can conclude that no one particular usage is "correct."
Based on Longman English Grammar, page 32, you can use participle constructions after there and it. However, it occurs in formal style.
It being a bank holiday all the shops were shut. (i.e. As it was ...)
There being no further business I declared the meeting closed. (i.e. As there is ...)
That remains true with subjects other than it and there, too. In other words it's going to be very formal to use participle clauses with different subjects as in
(With) Mrs Jones going to New York, Mr Smith took up her position.
Source: English Grammar Online
As P. E. Dant well pointed out, there is nothing specific to the verb form "being". you can use other verb forms in your participle which do not share the same subject as the one of your independent clause although it's not common use. It's simply very formal.
(By the way, I didn't know that. Thanks for asking this question. It made me learn something new)
Best Answer
"My book is different from your book" is correct. "Different" can't "accompany" in these examples (referring to "with"), and it doesn't convey a part of a whole (referring to "of"). It serves as a distinction (which is "from").
Here are definitions of each to help you better understand:
With
From
Of