"By yourself" means unaccompanied. "Alone" means the same but usually implies that you wish you were not alone.

What is the difference between alone and by myself?

To sum it up, the difference between "alone" and "by himself" is that the first means that someone is not on purpose on their own and the latter means that the person chose not to be with anyone else.

Is it correct to say by your own?

By yourself and on your own are two phrases that may look different, but their meanings are essentially identical. Both are used to say that you've done something alone, rather than with others.