In Wikipedia it says that if the Wronskian of two function is 0 everywhere it does not imply they are linearly dependent.
However, in books treating differential equations it seems that, if the two functions in question are solutions of a linear differential equation, then the condition $W=0$ does indeed imply they are linearly dependent.
In the web I found only that if two function are real analytic the condition $W=0$ guarantees their dependence, but there is no reason a solution to a linear ODE should be real analytic.
So I'd like to find a rigorous proof, possibly for the more general case, with $n$ functions.
Thank you in advance