Grammarly.com keeps warning me about passive voice. For example, in the following sentence it tells that I misused passive voice.
The long-standing problem of anti-social behaviour of some youngsters should be solved. It cannot, however, be solved by confinement.
I do not know who should solve this problem. So I used passive voice. Is it wrong?
Grammar checkers cannot know when the passive voice is appropriate or not. In many cases, they can't even identify the passive correctly. You should always treat such advice skeptically.
Even worse, simple-minded style guides like The Elements of Style have convinced many writers and educators that the passive voice is always bad, when of course that is false. So advice from native speakers about the passive voice cannot always be trusted.
You seem to have identified the appropriate guideline. If the agent of solve is irrelevant to the context or cannot be known, then the passive might be the best choice.
Furthermore, if the topic of the passage is problem, then a structure that makes problem the grammatical subject is probably a good choice.
Your sentences are both fine. You could replace the second one with
Confinement, however, cannot solve it.
My opinion is that this is neither better nor worse than your version.
My suggestion would be to stop using Grammarly, or at least be prepared to ignore it occasionally.
You could have written;
'Someone should solve the long-standing problem of anti-social behaviour of some youngsters. However, confinement is not the solution.'
I prefer your version of the first sentence. My suggestion for the second avoids repeating the 'be solved' construction. Sometimes repetition adds useful emphasis, sometimes it jars as merely repetitive. Your call!
(In the preceding paragraph, I first wrote 'My version of the second...' then changed it to 'My suggestion for the second...'. Do you see why? Do you agree? You don't have to!)
Word's grammar checker doesn't go in for this depth of analysis. It just detects a passive construction and flags it as possibly unnecessary. Very often this is a helpful heads-up. But it's a suggestion, not an instruction.
Grammarly.com keeps warning me about passive voice. For example, in the following sentence it tells that I misused passive voice.
No, it just tells you that you used it. Grammarly does not have the capability of distinguishing proper use of passive voice from its misuse.
That said, I find the phrasing a bit awkward, but not because it's passive voice. A problem is, by definition, something that should be solved, so saying "this is a problem that should be solved" is redundant. Also, "some youngsters" is rather vague. A better phrasing would be "There is a long-standing problem of anti-social behavio[u]r among youngsters. This problem cannot, however, be solved by confinement."
