Is the Sign of the Wronskian Arbitrary in Differential Equations?

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SUMMARY

The discussion centers on the Wronskian in differential equations, specifically addressing the issue of its sign being influenced by the order of functions. The participant confirmed that both functions were solutions and calculated a nonzero Wronskian. However, points were deducted due to a discrepancy in the sign, attributed to the ordering of the functions y1 and y2. The conclusion is that while the sign of the Wronskian is indeed arbitrary based on function ordering, it is essential to adhere to the conventions set by the grading rubric.

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  • Understanding of differential equations and their solutions
  • Familiarity with the concept of the Wronskian
  • Knowledge of function ordering in mathematical notation
  • Basic calculus skills, particularly in differentiation
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  • Research the properties of the Wronskian in differential equations
  • Study the implications of function ordering on mathematical results
  • Learn about grading rubrics in mathematics assessments
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Students studying differential equations, educators grading mathematics assessments, and anyone interested in the nuances of mathematical conventions and their implications on grading.

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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?
 
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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.
 

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