Let $u$ and $v$ be two solutions of the differential Equation
$y^{"} + P(x)y^{'} + Q(x)y = 0$ on $[a,b]$, Let $W(u,v)$ denote the Wronskian Of $u$ and $v$ Then
(a) $W(u,v)$ vanishes at point $x_{0} \in [a,b]$ $\implies$ $u,v$ are Linearly Dependent.
(b) $W(u,v)$ is identically zero on $[a,b]$ $\implies$ $u,v$ are Linearly Dependent
Now ,I Know from this question Proof that ODE solutions with Wronskian identically zero are linearly dependent That option (b) must be correct.
For option (a) We know that Wronskian for Differential Equation is either identically Zero or Never Zero, so if Wronskian vanishes at one point $x_0 \in [a,b]$ it must vanish identically in $[a,b]$ so option (a) is also correct.
So both options (a) and (b) must be true for this question.
Is My answer correct ?