Given an RL circuit, it starts with an initial condition. 

KVL defines a first order homogeneous ordinary differential equation with constant coefficients:

$$ 
	L \frac{di(t)}{dt} + Ri(t) = 0
	\to
L \frac{di(t)}{dt} = -Ri(t)
$$

Steps for solving RC natural response circuits:
1. Determine the initial inductor current, $I_0$, by analyzing the circuit for $t < 0$.

 2. Calculate the time constant, $\tau  RC$, where $R$ is the equivalent resistance connected to the capacitor for $t \ge 0$. 

3. Write the equation for the capacitor voltage:
$$ v(t) = V_o ^{e - \frac{t}{\tau}}, t \ge 0  $$
4. Calculate other quantities of interest using the capacitor voltage

- The *natural* response of a circuit is where there is an initial condition, but nothing else is driving the circuit.
- The *step* response of a circuit describes the behavior of a circuit when a sudden change is introduced (switch toggled, et cetera)