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Thank you, this remark:
I see. Well, if are differentiable, then linear independence implies for all . If they are not both differentiable, then it is possible that they are linearly independent yet . See http://en.wikipedia.org/wiki/Wronskian# … dependence for an example.
Of course but what i meant was: can I avoid to include W(t0)!=0 for some t0 in my hypotesis? In other words, if I have two linearly independent solutions u and v, can I automatically say W(u,v)!=0 for all t?
Yes, if you can show that for some then for all .