I need to show that $y(t) = t$ and $g(t) = t \ln(t)$ are linearly independent. I thought I could use the Wronskian as follows:
$y'(t) = 1$
$g'(t) = 1 + \ln(t)$
So $W(y, g) = (t)(1 + \ln(t)) - t \ln(t)$, so $W(y, g)(0) = 0$, which means they're not linearly independent. Am I doing something wrong, or is the problem statement written incorrectly?