What exactly is steady-state solution? In solving differential equation, one encounters steady-state solutions. My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when $t \rightarrow \infty$. 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?

A Steady State Solutions is the long term response of a system and hence is not dependant on the initial conditions. 
It can also be referred to as the Particular Integral. 
