Solving v''t + v' = 0

When I substitute w for v' I get

$\displaystyle \frac{dw}{w}=-\frac{dt}{t}$

$\displaystyle ln(t)=-ln(w)+c$

but this gives me $\displaystyle w=-t/c \rightarrow w=t/c$ rather than $\displaystyle w=c/t$

A seemingly simple separable equation that I am getting hung up on.