expression
by some chance; somehow; in some way
Used when something happens unexpectedly or by coincidence, often with a sense of 'I don't know how, but...'. Common in casual speech.
どうかして彼の秘密を知ってしまった。
By some chance, I ended up learning his secret.
どうかしてうまくいった。
Somehow it worked out.
expression
somehow or other; one way or another; by any means
Expresses determination to accomplish something regardless of the method, similar to 'by hook or by crook'. Often used with volitional or imperative forms.
どうかしてこの問題を解決しなければならない。
We must solve this problem one way or another.
どうかして彼を説得してみせる。
I'll persuade him by any means possible.