Given three functions: $$y_1=x+1 ,y_2=x^3 , y_3=e^x$$ The Wronskian of these three functions at $x_0=0$ is $0$. However the Wronskian at $x_0=1$ is $e$.
Examining the domain $[-2,2]$ the Wronskian is both zero and non-zero over the same domain. How is this possible?