  Recently, we have studied a delay differential equation which has a
coefficient that is a linear function of time. The equation has shown the
oscillatory transient dynamics appear and disappear as the delay is increased
between zero to asymptotically large delay. We here propose and study another
equation that shows similar transient oscillations. It has an extra exponential
gaussian factor on the delayed feedback term. It is shown that this equation is
analytically tractable with the use of the Lambert $W$ function. This equation
is also studied numerically to confirm some of the properties inferred from the
analytical solution. We also have found that the amplitude of transient
oscillation changes and goes through a maximum as we increase the value of the
delay. In this sense, the proposed equation is one of the simplest dynamical
equations that brings out a resonant behavior without any external oscillating
inputs.
