# Is Wronskian sign arbitrary?

1. Mar 20, 2013

### 1MileCrash

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?

2. Mar 20, 2013

### fzero

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.

3. Mar 25, 2013

### 1MileCrash

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.