I am taking a math course this semester and the problems that are given to us on a weekly basis require less than half a page to solve. The path to the proof is relatively straightforward, using the things we learned in class. However, my professor is accusing me of cheating because my proofs look very similar to online solutions. I don't know what to do because the proofs do look similar, even if they aren't word for word, but I wouldn't know any other way of solving them using the information we learned in the course.
Because the problems were relatively simple, there doesn't seem to be many places where I could "branch" off and do something completely different from what can be found online. What do you think is the best course of action in the face of this allegation?