Definition:Steady-State/First Order ODE

Definition
Consider the Decay Equation:
 * $\dfrac {\d y} {\d x} = k \paren {y_a - y}$

where:
 * $k \in \R: k > 0$
 * $y = y_0$ at $x = 0$

which has the particular solution:
 * $(1): \quad y = y_a + \paren {y_0 - y_a} e^{-k x}$

The term $y_a$ is known as the steady-state component of $(1)$.

Electronics
The term is often seen in the context of the current in an $LR$ electric circuit $K$:

Also see

 * Definition:Transient