If someone want to do something and I don't want to help him can I say: 'cope alone'?
ex: A- I don't know how to get there. Can you help me?
B- You're not a child anymore! Cope alone!
I tend to differentiate between "alone" and "on your own" - "alone" would be how I would describe, for example, someone who lives in a house/flat with no other people (He lives alone), or that someone perhaps went somewhere without anyone else (He went on holiday alone). I would use "on his/your/etc own" to mean "without anyone else's help" (He built that bookcase on his own).
That's not a hard and fast rule, by the way, just how I think I use the two phrases.