Time varying voltages
They're not DC.
Distinguish time-varying voltages and currents vs. steady-state response to sinusoidal excitation.
The latter is much more restrictive (less general) than the former, but using AC analysis techniques allows vast simplification in many cases.
It may be difficult or impossible to find closed-form solutions in relatively simple situations of transient analysis because you have to find solutions to a differential equation, which is not necessarily straightforward.  Of course in modern times we often use numerical solvers (such as the SPICE engine) which can give us very useful answers in transient and nonlinear situations.