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Known to me examples of L.I. functions having Wronskian=0 have also product=0. One such example was manufactured by Peano about 1890. By the way: Analytic functions with a zero Wronskian are linearly dependent - done by Bucher in 1900. I have a proof which is a bit simpler than Bucher`s and has less than 2 pages.

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  • $\begingroup$ When you say 'having $W=0$' do you mean over a whole (non trivial) interval? $\endgroup$
    – Git Gud
    May 13 '13 at 20:32
  • $\begingroup$ Do you mean like the Note on page 2? $\endgroup$
    – Amzoti
    May 13 '13 at 21:03
  • $\begingroup$ Yes, over any open interval $\endgroup$ May 15 '13 at 15:50
  • $\begingroup$ Your Note on p.2 states Peano's example. $\endgroup$ Jun 5 '13 at 13:12

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