# Find two linearly independent functions with a zero Wronskian but a nonzero product.

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.

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