Leak detection
I have no idea of the going rate for electronic leak detection. I'm sure it won't be cheap, but nothing is. As to finding it yourself, sure you can. It will require digging down to the pipe and uncovering it until you find it. How deep is the pipe buried, what type of soil do you have, and your personal ability to do that type of work. If I were going at it, I'd try to determine as close as possible where the water seems to be coming up. Then I'd dig down to the pipe and uncover a couple of feet or so. Then you should be able to tell which side of you hole the leak is by where the water is coming into the test hole. What make this a "fun" job is the muck that makes digging a real b....h! Once you find the leak and uncover it, the task of repair remains. Now you have to figure out what caused it. It could be a poor solder connection or it could be any of a number of things. Try to remedy the cause before you repair. Cut the leak out, then cut a repair piece that will fit exactly in the opened space. Clean the pipes with emery cloth, apply flux and slide a coupler (the kind that do not have the stop nub in the center) over each end of the repair piece and put it in place. Flux the other two pipe endsand work the coupler over them. It would be wise to mark on those two pipes just how far you need to slide the couplers. Then solder all 4 joints. Now it's possible the pro plumbers have a better system, but that would work. The other way to do the job is to write a check.