In theory, when a constant voltage is applied to a coil, the current will start to increase linearly. That increasing current means a variable magnetic flux, which will induce a voltage in the secondary.
So if all resistances are 0, when a constant DC voltage is applied at the primary, a constant DC voltage will be seen at the secondary output. Seems strange, I know, because in practice we never have zero resistances and ideal voltage sources.
For example, in this LTspice simulation, for the series Rs = 1 ohm, we see the Vout spike (in red) we expect from practice.
In the next plot (in yellow), Rs is only 1 miliohm, and the Vout is almost constant in all the 100 seconds plotted. Then, for Rs = 1 microohm (the green plot), the Vout is even closer to a constant 10V output.
If Rs were to be precisely 0 ohms, then the Vout will stay at precisely 10V forever.