Durbin Watson Test -- PLEASE HELP!

Can the Durbin Watson test be used for first-order AR models? I’ve noticed that some places in the curriculum says yes and other answer explanations say you cannot use DW test for any model with a lagged variable…

Y is not a lagged varaible of itself but a function of time
log of sales = b(o) + b(1) x time
level of sales is function of time
Drurbin watson ok

Y is a lggaed variable of iteslf
sales ths month = b(o) x b(1) x sales last month
level of sales depends on last period sales
Durbin watson no use