Yes, the four gospel writers are inspired of God and provide different but not contradictory details of the life of Jesus. Inspiration does not mean they must have identical accounts. Inspiration means they have different but not contradictory accounts. When put together, they complement nicely and fill in details the others leave out. Let's consider the example of an accident. If one witness stands to the north side of the accident, he sees the accident from his vantage point. Now the other witness stands on the south side, the opposite side of the street, he sees different details because of his angle. Now would both men have identical accounts? Of course not, the one on the south side cannot see what happens on the north side of the accident nor can the man on the north side see what happens on the south side. However, when you put the two accounts together, you get a more complete picture of the accident. Both men include different details but they should not be contradictory.
That is what we have in the gospels. The writers include different, but not contradictory, details. Inspiration does not mean the four gospels must be identical in every way. That would be quite boring to read four accounts tht are exactly the same. Each writer includes details he feels are necessary for the audience he is addressing. Matthew, writing to the Jews, must include all the Old Testament prophecies, while Mark, writing to the Greeks, does not include many prophecies but writes on the action of Jesus' life. Is that a contradiction? No, it's just that each writer included details he felt were necessary and left out others he felt would not be necesary for his audience. Alleged contradictions are explained when one studies the accounts and puts each event of Christ in its chronological order.
Matthew records one angel, Luke and John record two. The answer is this. Where there are two there must be one. Get it? There were two angels at the tomb but Matthew only writes about one in his account. Is this a contradiction? No, because where there are two, there must be at least one. Luke includes two, but Matthew only includes the one that spoke with Mary. He keyed in on that one and left the other angel out. Luke and John include the other one. We do that in our reporting. If Clinton and Gore appear on the podium but only Clinton talks and Gore says nothing, some newspapers will say "Clinton appeared and said such and such" and not mention Gore. Other papers will say, "Clinton and Gore appeared and Clinton stated ...." Is there a contradiction? No, just some reporters mentioned one person while another chose not to.
Hope this helps. Keep studying the word!