Is the word desenhou the same in Brazilian and European Portuguese?

Yes

The word "desenhou" is identical in meaning, spelling, and grammar in both Brazilian and Continental Portuguese. The only difference is in pronunciation. In Brazilian Portuguese, the unstressed vowels are generally more "open" and clearly articulated. In Continental Portuguese, unstressed vowels (such as the "e" in de-) are often "closed" or reduced, which can make them sound much shorter or nearly silent to a Brazilian speaker.

Brazilian Portuguese Examples

1. Ele desenhou um cachorro no papel. (He drew a dog on the paper.)
2. A menina desenhou um sol bem grande. (The girl drew a very big sun.)
3. O professor desenhou a fórmula no quadro. (The teacher drew the formula on the board.)
4. Ela desenhou um coração no caderno. (She drew a heart in the notebook.)
5. Meu amigo desenhou um carro de corrida. (My friend drew a racing car.)

Continental Portuguese Examples

1. Ele desenhou um cão no papel. (He drew a dog on the paper.)
2. A menina desenhou um sol muito grande. (The girl drew a very big sun.)
3. O professor desenhou a fórmula no quadro. (The teacher drew the formula on the board.)
4. Ela desenhou um coração no caderno. (She drew a heart in the notebook.)
5. O meu amigo desenhou um carro de corrida. (My friend drew a racing car.)