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Is Wronskian sign arbitrary? 
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#1
Mar2013, 06:38 PM

P: 1,272

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
Mar2013, 10:36 PM

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P: 2,606

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
Mar2513, 09:38 AM

P: 1,272

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. 


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