On your own = Without any help; unaccompanied by others; alone
By yourself = Through one’s own efforts; alone; nobody else
On your own and by yourself are two phrases that are seemingly different, but their meanings are the same and often both are used interchangeably with no loss of meaning. However, one may be preferred over another, according to context. Again, it all depends on the context:
I handled the situation on my own. (conveys a positive approach which one’s proud of)
I handled the situation by myself. (shows a negative one since nobody was there to help one, so he had to do it by himself).
Both on my own and by myself may denote ‘without assistance from anybody else’. On my own implies ‘on my own initiative, without being prompted or ordered to do so,’ whereas by myself may suggest ‘when I was alone:’
On your own:
We are expecting our first baby earlier this month and I have to do things on my own.
These exercises are very simple; Jack can do these all on his own.
She has been in the city for quite some time and now is used to live on her own.
The matter has become so complicated. Can you handle it on your own?
He had his right arm in plaster so, couldn’t tie his shoelaces on his own.
It is not safe to go and come back late at night in this city on your own.
He thought of the idea of participating in the quiz contest on his own.
With all these picturesque rocky shores, I really enjoy spending a quiet evening here by myself. (alone)
You can’t lift the box onto the table all by yourself! Can I help you? (through one’s own efforts alone).
Though she is ill enough for a doctor to be called, she likes to visit him by herself.
Jack hesitated to drive into a dark and vacant road by himself.
She occupied by herself the parking space large enough for two cars.
Pamela is unable to download it by herself since this is new to her.
Little Tanya made that paper boat all by herself.
Why did you let your wife go by herself such a far-off place?
He’s been living by himself since he’s broken up with Susan.
Little Jimmy slipped on the wet floor but stood up by himself.
Jill arrived late in the class to find the teacher by himself chit-chatting with another teacher.