Moj brat je juče bio u bolnici.

Because moj has to agree with brat in gender, number, and case.

• brat is masculine
• singular
• nominative

So the correct form is moj.

Compare:

• moj brat = my brother
• moja sestra = my sister
• moje dete = my child

Je is the 3rd person singular present form of biti = to be, and here it works as an auxiliary verb.

Serbian usually forms the past tense with:

present of biti + past participle

So:

• je bio = was / has been

In this sentence, English naturally translates it as was: Moj brat je juče bio u bolnici. = My brother was in the hospital yesterday.

Bio is the masculine singular past participle of biti.

It agrees with the subject:

• brat is masculine singular
• so the participle is bio

Compare:

• Moj brat je bio = My brother was
• Moja sestra je bila = My sister was
• Moje dete je bilo = My child was
• Moja braća su bila / bili depends on meaning and group composition

So bio is there because the subject is a singular masculine person.

Because je is a clitic. In Serbian, clitics usually go near the second position in the clause, not at the very beginning.

So Moj brat je... is the normal order.

This is why Serbian word order can look different from English. The sentence is not built word-by-word like English My brother was yesterday...; instead, the clitic je tends to come early, after the first phrase.

No. Juče = yesterday is fairly movable.

This sentence is natural:

• Moj brat je juče bio u bolnici.

But these are also possible:

• Juče je moj brat bio u bolnici.
• Moj brat je bio juče u bolnici.
• Moj brat je bio u bolnici juče.

The meaning stays basically the same, but the focus or emphasis changes slightly. The version you were given is a very normal neutral order.

Bolnici is the locative singular of bolnica = hospital.

After u when it means in / inside / at a location, Serbian uses the locative:

• bolnica = hospital
• u bolnici = in the hospital

The ending -i is the normal locative singular ending for many feminine nouns like bolnica.

Because Serbian makes an important distinction:

• u + locative = being in a place
• u + accusative = motion into / to a place

So:

• bio u bolnici = he was in the hospital
• išao u bolnicu = he went to / into the hospital

That is why your sentence uses u bolnici: it describes location, not movement.

Because Serbian has no articles like English a/an/the.

So Serbian simply says:

• u bolnici

and English decides whether that should be:

• in a hospital
• in the hospital

based on context. In this sentence, in the hospital is the most natural English translation.

Not necessarily.

U bolnici literally tells you that he was in / at the hospital. Context decides more.

It could mean he was:

• a patient
• visiting someone
• working there
• there for some other reason

Very often people will understand it as he was in the hospital in the ordinary sense, but the phrase itself does not strictly force that meaning.

Sometimes yes, if the context already makes it clear whose brother you mean.

But moj brat is completely normal and natural.

Serbian often avoids repeating possessives when the relationship is obvious, and you may also hear:

• Brat mi je juče bio u bolnici.

That also means My brother was in the hospital yesterday.

So moj brat is explicit, while other versions can sound a bit more conversational or context-dependent.

Not exactly. Serbian je bio is the normal past tense form here, and in this sentence English translates it as was.

Serbian perfekat often covers situations where English uses the simple past, and sometimes where English uses have + past participle. The exact English translation depends on context.

Here, because of juče = yesterday, English must use was, not has been:

• My brother was in the hospital yesterday.
• not My brother has been in the hospital yesterday.

So the Serbian form is fine; the difference is mainly in how English and Serbian handle past-time expressions.