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If the Wronskian equals 0, is it always 0?

  1. Sep 13, 2015 #1
    If the Wronskian of a set of equations equals 0 over a particular interval in the functions' domain, is it possible for it be non-zero under another interval? Are there any particular proofs for or against this?
  2. jcsd
  3. Sep 14, 2015 #2


    Staff: Mentor

    It took me a very long while to find a good example, but I found one in, of all places, "Advanced Engineering Mathematics", 3rd Ed., by Erwin Kreyszig.
    Consider the three functions: ##y_1 = x^3, y_2 = |x|^3, y_3 = 1##.
    ##W(y_1, y_2, y_3)## is identically zero on one interval (implying that the three functions are linearly dependent on that interval), but ##W(y_1, y_2, y_3)## is different from zero on another interval (implying that the three functions are linearly independent on that other interval). I leave it to you to figure out what intervals we're talking about here.
  4. Sep 14, 2015 #3
    Thank you! :D
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