When I have time I will add "Differential Drive" as a tutorial to explain the pros, cons, and misunderstandings that often go along with the term.
Here is my condensed version for now...
The term "differential drive" refers to a mechanical system that allows the wheel on the inside of the turn to drive at a rate lesser than the wheel on the outside, which is required so that there is no skidding or wheel drag happening . Here is a great article to read...
https://en.wikipedia.org/wiki/Differential_(mechanical_device)
So my first point shall be...
"you are probably NOT referring to an actual differential".
Any trike you have seen with dual rear wheel drive is most likely NOT a differential, but in fact a "ratcheting drive".
The great video Twinkle just posted is a perfect example of a ratchet drive. That is NOT a differential drive.
A ratchet drive is
completely different than a differential, so much in fact, that is actually does the
opposite, making only the wheel on the inside of the turn do all of the work. The reason is because the other wheel is turning faster, engaging the ratchet, which disengages the drive via the pawls.
A ratchet drive therefor has no real use on a trike, as the only time both wheels are "driven" is when going in a 100% straight line.
Some may argue that "but I need the grip", but this is totally false. I dare you to spin your trike tires!
Now back to the "true differential". These are complext and VERY expensive to make, as those who have pulled the cover off their auto diff. can attest to. There are a lot of moving parts, and to this date I have ever only seen one made for bicycle usage, and it was a beast made for rickshaws.
Ok, so lets recap up to here...
1) There are no true differential drives available for trikes.
2) Ratcheting drive offers no advantages whatsoever.
I am not saying this just from googling the subject either. I have bult many ratchet drive trikes, including that funny 1982 car seat trike I posted in my last response. Ratchet drive does work, but has no advantages over one wheel drive at all.
So to answer what is usually the last question...
"but won't my trike push to one side with only one wheel drive?"
Nope.
There is absolutely no noticeable effect on steering or forward movement on any single wheel driven trike or quad.
If you rode each one you could not tell the difference. No way, no how.
So this leaves only one answer.... not worth the cost of effort.
I will do this in much more detail later, showing some diagrams of both types of drives as they move around corners and such.
Now having said all of that... build it anyway, post photos, and then your ride report, that's what DIY is all about!!
If I had not built several myself, I would still do so after reading all of this. Just like a rear steer bike (other can of worms)!
Brad