on my own

I have collected the followings from various sources as your site.

I would like to study them accurately. so, would you tell me, as a native speaker, if they are right, if so, would you add them what you think of I should learn?

You would say, 'I want to find out about it on my own.' But you wouldn't say 'by myself' because 'on my own' means for myself, and not just 'by myself.'

You could say 'I went swimming by myself', and that would mean that there was no one there swimming with you. But if you said that you went swimming on my own, that could mean that you didn't ask anyone to go swimming with you, that you wanted no company with you.

So by myself indicates that you were alone by chance and on my own means that it was a decision you made to be alone.

' alone' and 'by myself' are more or less interchangeable although, 'alone' is more emotive (it is an adjective after all~).
' by my own' has a similar meaning to 'alone' and 'by myself' but it is not the same. 'by my own' is usually part of phrases such as 'by my own means' which means that you will use your own resources (like money) to acheive something.
For example 'I can do it by my own means'
Another way to say 'by myself' or 'alone' is 'on my own'. They all mean the same thing

• If you want to say that you and your friends are okay doing something by yourselves you would say;
'We are fine by ourselves/on our own'

If you are doing it alone then you say;
I can do it by myself/on my own/alone'

I can do it' and 'I am fine' are more or less interchangeable

Many thanks