For Wronskian determinant, $y_1$ and $y_2$ is the fundamental set of solution if **W** is not 0 (for all $t$?)

But, if **W** could be 0 for some t, does the statement still hold?

Particularly in the real equal root example:

$y''$- $2y'$ + $y$ = 0

$y_1$ = $e^t$

$y_2$ = $t$$e^t$

$W = t^2 e^{2t}-t e^{2t} = 0$ if $t=1$ or $0$ WRONG

How to think about this kind of situation? if there is no restriction on $t$