On my DE test, I was asked to determine if two solutions to a DE are fundamental solutions. So I confirmed they were both solutions, and took the Wronskian, which was nonzero. I got points marked off, and he put a minus sign in front of my wronskian result. Isn't the sign of the Wronskian determined by what function I call y1 and what function I call y2 and is thus completely arbitrary?
Yes the sign on the Wronskian is determined by the ordering that you assign to the functions. It's a weak excuse, but the grader was probably just comparing your answer with their solution sheet and saw the sign difference and didn't think about why they were different.
Well, I looked at the test and on the paper the functions were called y1 and y2 already, and in my work I did write W[y1,y2] = my wronskian. So I guess I can understand. I don't think I'll argue this one. I noticed that the wronskian order is arbitrary early off and have just been taking the easier derivative first.