TITLE: If the Wronskian of two functions is zero then these functions are LD
QUESTION [7 upvotes]: I'm studying a book of differential equations which says that if the Wronskian of two functions is zero then these functions are linearly dependent. the author doesn't prove it, he simply said as a easy consequence of basic properties of determinants, I tried to prove by myself without success. 
I need help.
thanks a lot.

REPLY [7 votes]: The statement holds if $f_1$ and $f_2$ are solutions of a linear differential equation. The functions $x^3$ and $|x|^3$ are linearly independent in any open interval containing $0$, but their Wronskian is identically equal to $0$.