What exactly is steady-state solution? In solving differential equation, one encounters with steady-state solution. My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when t -> infty. But the steady-state solution is given as f(t), and this means that the solution is a function of t - so what is this t being in limit?
Steady state means some properties of the system are unchanging wrt to time. It usually occurs after some time the process is initiated. Corresponding solutions are the steady state solutions.
Example from dynamics: You can picture for yourself a cantilever beam which is loaded by a force at its tip say: F(t)=sin(t). At t=0 the force is applied, then you get the transient state, after some time the system will become in equilibrium: the steady-state. In this state no changes are applied to the system. You can expand this thinking to other differential equations as well. Hope that helps.