  We present a new approach to examine transient dynamics in a class of
non-autonomous delay differential equations. Exact solutions for these
equations are obtained using the Lambert $W$ function alongside an
appropriately chosen initial function. These solutions provide a reliable
approximation for transient dynamics when the initial functions are not
markedly distinct. We explore a non-autonomous equation that exhibits a
distinctive phenomenon of reviving dynamics as an illustrative example. The
derived exact solutions effectively encapsulate the qualitative characteristics
of this reviving dynamics over various delay values.
