Some questions about the Wronskian:
If I want to check out if two functions are linearly dependent I use Wronskian.
My question is : If I find $x_0\in I $ such that $W[f_1,f_2]\neq 0 \implies$ the function are linearly independent ? But if I find $x_1\in I$ such that $W[f_1,f_2]=0$ it's not enough for proving the functions are linearly independent?
An example :
There is 2 function $f_1(x)=x,f_2(x)=x^2 \implies W[f_1,f_2](x)=x^2.$
$x=0 \implies W[f_1,f_2]=0$
I know both function are linearly independent.
I am a little confused ,Thank you !