ages ago I started a thread on something similar called 'firing on one cylinder - does it really matter' (sorry can't do links). I got some helpful and interesting replies. My oldest ds is definitely relaxed in his attitude to trying. I think this is ingrained in his personality so I can't change him totally.
So far my best way of coping with this trait is to give him the chance to try out lots of different activities, but also accept that some things are not 'him' and never will be - he has stared and left a few out of school clubs for instance. Much relief all round.
Also, some things, put down once, like a book, he will go back to months later. He's just reading 'Artemis Fowl' eagerly - a book he was give two years ago and gave up on. So I leave things lying about, saying under my breath 'never say never'
Regarding homework, as long as dh or I look over his work, and take lots of interest in it, he is usually motivated to do better. If we cease giving him that attention, he tends to do less. Hard work being a parent!