Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    Mark44

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: If the Wronskian equals 0, is it always 0?
Loading...