I was going to add a couple of things but I see they have already been mentioned. Lots of good advice.
My son is also stubborn, but so I am. So if I have it in my mind that something might be good for him (e.g. swimming) and that he shouldn't give up after the very first lesson, I make sure I try my best to convince him to stay.
So for example with swimming, the first reason I gave him was that it was an important skill to have and it would be useful for him when in future he went to a swimming pool, the sea, etc. When that obviously failed to convince him, I said he had to do it until he could swim confidently (let's say these many meters, or up to stage 6, or whatever your cut off point is). And then, as I knew it was hard for him and he needed extra motivation, I did things like have a nice treat for him after he was good at his swimming lesson, or earning points for each time it wasn't a battle to go swimming and he tried his best. Then at the end of the month, or the term, he could exchange those points for something that he really wanted (a nice toy, an outing, etc).
Also, each time he passed a stage, especially when it took it the longest and it had been the hardest, he got a nice reward after that.
The other thing I wanted to mention since you say your DS easily gives up things without even trying, is that my DS was the same. It happened with swimming (I didn't let him and now he is very happy and a confident swimmer). It happened with karate. It happened with rugby, and it happened with beavers (which other posters have already recommended to you).
But my best example (and I always use it with him for when he is nervous and reluctant to try something new) is Beavers. He was happy when I told him I got a place for him. He was very happy the first day. But then the following week he didn't want to go and protested, cried, begged me not to take him (same things he did with swimming). After talking with him and checking there was no other reason for his reluctance than him simply not wanting to continue, I made a deal with him and said give it a chance until the end of October (so that he could attend the pumpkin carving and Halloween party that I knew he would enjoy), and that if after those two months of going he still felt the same I would not force him to do it. He then calmed down, and agreed to give it a go.
Well, after only a couple of weeks he arrived home one day very excited and said Beavers was great and his favourite thing and that he always wanted to go. And to this day (he's been there almost 2 years) he is still very happy to go, enjoys it, and now cries if for any reason is not able to go. Completely turn around.